i 


Southern  Branch 
of  the 

Jniversity  of  California 

Los  Angeles 


L  1 


V3b 


This  book  is  DUE  on  the  last  date  stamped  below 


v 


Mi 

MAY  1  8  1951  i 

MAR  2  7 

1956 

Form  L-9-15m-8,'24 


METHODS 


IN 


ELEMENTARY   SCHOOL   STUDIES 


■*&&<&■ 


-v9   ^M   o 


u 


#7 


METHODS 


IN 


ELEMENTARY  SCHOOL  STUDIES 


A   BRIEF  OUTLINE 


BY 


BERNARD    CRONSON,  A.B.,  Pd.D. 

PRINCIPAL    PUBLIC    SCHOOL   NO.    125,    BOROUGH    OF   MANHATTAN 
CITY    OF   NEW  YORK 


7^7 


Wefo  gork 
THE   MACMILLAN   COMPANY 

LONDON:   MACMILLAN  &  CO.  Ltd. 
1906 

All  rights  reserved 

Ffc.3  1908 


COPYRIGIIT,    1905, 

By  THE   MACMILLAN   COMPANY. 


Set  up  and  electrotyped.     Published  December,  1905. 


NortoocU  19rrss 

J.  S.  Gushing  &  Co.  —  Berwick  &  Smith  Co. 

Norwood,  Mass.,  U.S.A. 


C£8 


CONTENTS. 


i 


I. 
II. 


III. 

IV. 

V. 

VI. 

VII. 

VIII. 

•  IX. 


Reading 
Dictation    . 

Spelling,  Punctu 
tai.s,   ETC. 

Composition 
Grammar     . 
Literature 
Nature  Study 
Geography 
History. 
Civica  . 
Arithmetic 


ation,  Paragraphing,  Capi- 


PAQB 
11 

24 


41 
63 

70 

87 

95 

103 

112 

120 


"Theory  alone  is  inspiring,  but  vague;  practice 
alone  is  definite,  but  formal ;  theory  combined  with 
practice  is  inspiring,  rational,  and  definite." 


PREFACE. 

A  knowledge  of  specific  methods  is  a  necessary 
preparation  to  the  art  of  teaching,  because  — 

1.  Method  is  the  medium  between  teacher  and  pupil. 
It  is  not  the  question  whether  the  teacher  understands 
the  rationale  of  the  processes  that  concerns  the  child, 
but  the  validity  or  the  falsity  of  the  method  employed. 
Teaching,  or  the  process  whereby  one  mind  causes 
knowledge  to  arise  in  another,  is  an  art ;  the  teacher, 
during  the  performance  of  his  task,  is  an  artisan ;  and 
as  such  he  should  know  how  to  use  his  tools,  namely, 
his  methods. 

2.  The  mere  study  of  the  science  of  education  does 
not  of  itself  insure  the  mastery  of  methodology  any 
more  than  theoretic  knowledge  in  any  other  field  car- 
ries with  it  also  skill  in  application.  Even  Ruskin, 
with  all  his  keen  insight,  would  scarcely  be  regarded 
as  a  competent  teacher  of  painting.  And  why  not? 
"  There  is  in  the  master's  profession,"  observes  J.  G. 
Fitch,  "the  same  difference  which  is  observable  in  all 
other  human  employments  between  the  skilled  and  the 
unskilled  practitioner,  and  .  .  .  this  difference  depends 
in  a  large  measure  on  a  knowledge  of  the  best  rules 


8  PREFACE. 

and  methods  which  have  to  be  used.  It  is  easy  to  say 
of  the  schoolmaster,  '  nascitur  non  fit,"  and  to  give  this 
as  a  reason  why  all  training  and  study  of  method  are 
superfluous.  But  we  do  not  reason  thus  in  regard  to 
any  other  profession,  even  to  those  in  which  original 
power  tells  most,  and  in  which  the  mechanic  is  most 
easily  distinguishable  from  the  inspired  artist." 

3.  The  study  of  the  science  of  education  and  the 
subsequent  deduction  of  methods  by  the  individual 
teacher  will  not  satisfy  the  demands  of  a  common-sense 
pedagogy,  because  — 

(a)  The  average  man  fails  to  trace  back  deductions 
to  their  underlying  principles  for  verifications,  and  rests 
content  in  the  belief  that  his  practice  is  in  accord  with 
his  theory.  The  teacher  is  no  exception,  —  he  masters 
his  science,  then,  blissfully  unconscious,  proceeds  with 
wrong  applications. 

(5)  It  takes  years  of  unaided  effort  to  build  up  a 
satisfactory  method,  and  if  we  take  into  consideration 
the  fact  that  the  number  of  years  thus  spent  in  prepa- 
ration is  greater  than  the  average  teacher  devotes  to 
his  profession,  it  will  be  readily  seen  that  the  benefits 
accruing  to  the  teacher  in  power  and  breadth,  not  to 
mention  freedom,  will  scarcely  offset  the  injustice  to 
which  the  child  is  subjected  during  that  period,  —  and 
the  child  has  a  right  to  object  to  being  made  the  subject 
of  experiment. 

4.  Nor  is  the  claim  valid  that  training  in  specific 
methods  unfits  the  teacher  for  spontaneous,  independ- 


PREFACE.  9 

ent,  characteristic  work.  "No  natural  educator,"  says 
\V.  Rein,  "is  so  gifted  through  divine  favor  from  the 
beginning  as  to  be  able  to  reach  the  highest  results 
entirely  without  the  aid  of  methodical  schooling,  and 
there  will  never  be  a  method  so  wonderful  as  to  be 
able  to  supplant  the  power  of  a  strong  personality.  .  .  . 
This  truth  must  nevertheless  be  advanced  against  the 
scorners  of  all  method :  even  the  most  happily  consti- 
tuted nature,  the  teacher  by  divine  grace,  is  not  re- 
stricted nor  rendered  ineffective  by  the  directions  of 
method ;  on  the  contrary,  his  activity  is  promoted  and 
insured  of  its  effectiveness."  There  is  indeed  no  more 
valid  reason  for  the  claim  that  the  study  of  method 
tends  to  suppress  the  individuality  of  the  teacher  than 
there  was  in  the  claim  that  the  teaching  of  penmanship 
by  printed  models  would  crush  the  individuality  of  the 
child's  handwriting.  There  is  more  in  human  nature, 
in  human  character,  in  the  human  mind  than  what  is 
put  there  by  the  pedagogue.  Nay,  more,  nature  will 
have  its  say  in  spite  of  him ;  so  that  the  student  with 
a  taste  for  investigation  will  not  renounce  his  work 
simply  because  such  work  has  been  facilitated  for  him ; 
while  he  who  is  not  so  inclined  will  certainly  not  be 
assisted  by  the  fact  that  the  study  of  methods  formed 
no  part  of  his  preparation. 


• 


I.  — UK  A  DING. 

There  are  three  stages  in  the  process  of  learning  to 
read :  the  first  aims  at  knowledge ;  the  second,  at 
power;  and  the  third,  at  fluency.  Each  stage  calls 
into  play  different  processes  of  the  mind  and  demands 
a  representative  mode  of  treatment  at  the  hands  of 
the  teacher. 

First  Stage  :  Presentation. 

The  purpose  of  the  early  lessons  in  reading  is  to 
familiarize  the  child  with  the  forms  of  certain  words. 
To  this  end,  the  teacher  chooses  familiar  and  simple 
words  or  sentences,  pronounces  them  before  the  class, 
and  writes  them  on  the  blackboard.  Attention  and 
repetition  complete  the  work. 

During  this  stage  no  attempt  is  made  at  analysis ; 
^  words  are  studied  as  wholes,  and  the  aim  of  the  lesson 
^  is  attained  when  the  child,  at  the  sight  of  the  symbol, 
^       recalls  readily  the  idea  it  stands  for. 

Second  Stage  :   Comparison. 

The  word-method  x  is  the  proper  vehicle  for  initiat- 
ing the  child  into  reading.     Symbol-recognition,  how- 

1  The  advantages  of  this  method  are  : 

1.  It  associates  the  unknown  written  word  with  the  known  spoken 
word. 

2.  It  accords  with  the  Culture  Epoch  Theory. 

3.  It  presents  material  for  inductions. 

4.  It  appeals  to  the  child's  utilitarian  tendencies. 

11 


<M 


12  READING. 

ever,  is  not  an  end  in  itself,  but  a  preparation  for  the 
more  serious  and  important  work  of  inducing  the 
phonic  elements  of  our  language  and  the  powers  of 
the  letters.  In  the  subsequent  lessons,  therefore,  the 
child's  attention  is  directed  to  the  comparison  of  words 
having  common  characteristics.  These,  in  obedience 
to  the  mind's  tendency,  gradually  dissociate  themselves 
from  the  words  of  which  they  form  parts,  and  become 
generalized  into  definite  symbol-sounds. 

As  a  brief  illustration  of  the  method :  The  child  who 
has  learned  to  recognize  as  symbols  some  such  words  as 

tar  fat 

car  fan 

far  for 

will  experience  but  little  difficulty  in  abstracting  the 
common  elements  and  in  assigning  to  each  its  appro- 
priate sound. 

Third  Stage  :  Application. 

THE   ART   OF   READING. 
Aim :   Thought. 

Means  :  Symbols. 

The  ultimate  aim  of  reading  is  thought-getting  ;  but 
as  this  presupposes  a  recognition  of  the  symbols  used 
in  conveying  thought,  the  teacher  must  bear  in  mind  — 

Fundamentals. 
1.    That    the    recognition    of    the    thought   and    the 
recognition    of   the    symbols    are  two   distinct   mental 
processes,  having  attention  as  their  common  factor. 


READING.  15 

2.  That  only  a  definite  amount  of  attention  is  avail- 
able for  any  given  period  of  time  ;  so  that  the  greater 
the  demand  is  on  the  child's  attention  for  symbol-recog- 
nition, the  less  of  his  attention  remains  to  be  expended 
on  thought-getting. 

3.  That  while  the  aim  of  reading  is  constantly  held 
before  the  child,  the  teacher  should  strive  to  give  him 
a  gradually  increased  proficiency  in  the  recognition  of 
the  symbols. 

4.  That  the  ideal  condition  obtains  when  the  means 
are  employed  automatically  in  the  attainment  of  the 
aim. 

Method. 

1.    Reading  by  the  child. 

By  throwing  the  child  upon  his  own  resources,  he 
will  eventually  gain  power  and  self-reliance. 

Aids : 

(a)  Syllabication. 

Teach   the   child   to  focus   his  attention    upon  each 
separate  syllable  of  a  word.     The  syllables  united  are 
impregnable  ;   divided,  they  yield.     It  is  only  in  this 
way  that  words  of  many  syllables  are  recognized. 
(5)  Comparison. 

Most  of  the  syllabic  elements  the  child  masters  dur- 
ing the  first  few  months  of  his  school  life.  If  he 
masters  also  the  powers  of  the  letters,  he  has  at  his 
command  all  the  means  whereby  he  may  decipher  any 
apparently  strange  syllable. 


16  READING. 

2.  Reading  by  the  teacher. 

The  child  listens  to  a  model  reading  lesson,  while  the 
teacher  takes  this  opportunity  to  clear  up  any  vague- 
ness in  the  content. 

3.  Thought-getting  and  repetition. 
(«)   Questions  by  teacher. 

(b)  Answers  by  pupils. 

The  teacher  asks  a  question,  making  it  brief  and 
pointed  ;  the  child  reads  the  answer  from  the  book. 
An  opportunity  for  variety  is  here  presented. 

The  exercises  up  to  this  point  have  been  in  the 
nature  of  a  preparation  ;  now  follow  : 

4.  Study  by  pupil,  preferably  in  the  class-room. 

5.  Reading  by  pupil. 

Model  Lessons. 
(a.    Report  of  a  lesson  in  a  3 A  grade.) 

"  The  wind  played  many  pranks.  He  lifted  many 
strong  men  off  their  feet,  and  set  them  down  in  the 
market  place.     At  length,  he  tired  of  this  kind  of  fun." 

1.  During  the  reading  by  the  child,  the  following 
words  were  developed  on  the  blackboard  : 

00 


(») 


Known 

Steps 

Unknoivn 

bank 

ank 

rank 

ranks 

pranks 

car 

ar 

mar- 

let 

et 

ket 
market 

READING.  19 

2.  The  teacher  read  the  selection,  questioned  upon 
the  meaning  of  "  pranks,"  and  commented  upon  "  He  " 
as  referring  to  wind. 

3.  Q.   Why  did  the  wind  stop  having  more  fun  ? 

A.  "At  length , fan." 

Q.  What  does  the  first  story  (or  sentence)  tell 

you? 

A.  "The  wind pranks." 

Q.   Give  an  example  of  his  pranks. 

A.  "He  lifted   market 

place." 

4.  Five  minutes  were  given  to  the  children  for  silent 
study  of  the  whole  lesson. 

5.  Reading  by  the  children. 

(b.    Report  of  a  lesson  in  a  5 A  grade.) 

"  A  peasant  once  had  a  faithful  horse,  who  had  grown 
old  and  could  not  serve  his  master  any  longer  ;  he  did 
not  care,  therefore,  to  provide  him  with  food.  So  he 
said  to  the  old  horse  :  '  I  really  do  not  want  you  any 
more,  for  you  are  of  no  use  to  me  ;  but  if  you  can  prove 
your  strength  by  bringing  me  a  lion,  I  will  keep  you  as 
long  as  you  live.  In  the  meantime,  however,  just  walk 
out  of  my  stable,  and  go  and  make  yourself  a  home  in 
the  fields."' 

1.  The  paragraph  was  read  aloud  by  a  pupil  and  the 
pronunciation  of  the  following  words  was  developed  : 

(a)  peasant,  by  comparison  with  pleasant. 

(b)  provide,  syllabicated  and  accent  noted. 


20  READING. 

The  study  1  of  unfamiliar  words  was  taken  up  at  this 
point  —  a  slight  variation  of  the  general  method. 

(a)  peasant. 

Q.  What  is  meant  by  a  "  peasant "  ? 

A.  (read  from  vocabulary).  A  peasant  is  a  coun- 
tryman. 

Q.  What  do  we  generally  call  a  countryman  who 
works  in  the  fields  ? 

A.  A  farmer. 

Q.   Who  will  give  one  word  for  "  peasant  "  ? 

A.  A  farmer. 

(6)  provide. 

Q.   Parents  provide  children  with   food.     What 

does  "  provide  "  mean  ? 
A.  "  Provide  "  means  give,  supply. 

2.  Paragraph  read  by  the  teacher. 

3.  Questions  asked  to  develop  the  thoughts  of  the 
paragraph  : 

Q.   Who  are  the  characters  in  the  story  ? 

A.  A  peasant  and  a  horse. 

Q.   Why  did  not  the  master  wish  to  feed  the  horse 

any  longer  ? 
A.  "  He  had  grown  old any 

longer." 
Q.   Had  the  horse  served  his  master  well  before 

he  became  old  ? 
A.  "A  peasant  once  had  a  faithful  horse." 

1  An  example  of  correlation. 


READING.  23 

Q.  What  did  the  farmer  tell  the  horse  to  do  ? 
A.  "Just   walk    out in    the 

fields." 
Q.   What  could  the  horse  do  to  get  back  ? 
A.  "If  you  can  prove as  you 

live." 

4.  Paragraph  studied  silently  by  class. 

5.  Pupils  called  upon  to  read,  others  to  reproduce 
orally.1 

1  Correlation. 


II.  — DICTATION. 

Aim :   To  represent  thought  in  correct  written  form. 
Topics  included : 

1.  Spelling.  5.  Abbreviations. 

2.  Homonyms.  6.  Paragraphs,  Stanzas. 

3.  Capitals.  7.  Letter  Forms. 

4.  Punctuation.  8.  Use  of  Dictionary. 

SPELLING. 

Aim:   To  represent  words  according  to  fixed  forms. 

Spelling,  as  the  art  of  recording  sounds  by  means  of 
symbols,  has  for  its  basis  the  recognition  of  elementary 
sounds  and  their  representative  signs  or  letters.  In  a 
phonic  language,  analysis  and  comparison  suffice  for 
the  study  of  its  spelling  ;  in  the  English  language,  how- 
ever, its  spelling,  though  based  on  rational  grounds, 
presents  so  many  anomalies,  that  the  memory  must  be 
called  upon  to  assist  the  other  two  processes. 

Fundamentals. 

1.  Analysis  is  the  basic  process  in  spelling  —  the 
human  mind  must  first  recognize  and  hold  in  attention 
the  syllable  before  it  can  determine  the  elements  of 
which  it  is  composed  and  the  symbols  which  represent 
them. 

24 


DICTATION.  27 

2.  The  analytico-synthetic  method  should  by  em- 
ployed in  spelling  —  word,  syllable,  letter,  word. 

3.  Each  spelling  word,  when  lirst  presented  for 
study,  should  be  introduced  in  a  sentence. 

4.  Each  spelling  lesson  should  include  both  an  oral 
and  a  written  exercise  —  the  former  for  study,  the 
latter  for  testing. 

5.  Rules  for  spelling  should  be  learned  inductively 
and  applied  deductively. 

6.  The  greater  the  number  of  the  association  links 

as  the  result  of  the  activity  of  the  various  senses,  the 

readier  the  recall. 

Method. 
Oral  Spelling : 

1.  The  word  is  first  pronounced,  then  written  on  the 
blackboard,  syllabicated  by  vertical  lines,  and  its  accents 
marked. 

2.  Individual  children  are  then  called  upon  to  spell 
as  follows : 

(a)  The  word  pronounced. 
(5)  »The  first  syllable  pronounced. 
(<?)    The  first  syllable  spelled. 
The  remaining  syllables  having  been  treated  like- 
wise, there  follows : 

(d~)  The  word  pronounced. 

3.  The  children  with  arms  extended  in  front  of 
them,  and  with  fingers  pointing  to  the  word,  write  it 
several  times  in  the  air,  while  the  teacher  signals  each 
new  letter  by  counting. 


28  DICTATION. 

4.    The  same  exercise  with  eyes  closed. 
Written  Exercise : 

1.  Words  dictated. 

2.  Words  spelled,  one  pupil  at  the  same  time  writing 
them  on  the  blackboard. 

3.  Errors  noted  by  drawing  a  line  through  the  word. 

4.  Papers  collected  and  returned. 

5.  Corrected  forms   written    above   the    errors   and 
below  the  exercise. 

6.  Study  and  recitation  of  corrections. 

General  Remarks. 

1.  A  dictation  should  accompany  each  spelling  exer- 
cise. 

2.  Each  day's  spelling  lesson  should  include  the  new 
words  of  the  previous  day. 

3.  The  spelling  of  words  whose  meanings  are  not 
known  is  a  waste  of  time  and  energy. 

HOMONYMS. 
Method. 

1.  Teach  through  the  medium  of  the  sentence. 

2.  Teach  one  word  of  a  group  at  a  time. 

3.  When  the  words  of  a  group  have  been  mastered 
separately,  they  should  then  be  compared. 

4.  Test: 

(a)  Write  sentences  on  blackboard,  omitting  the 
homonyms,  and  require  pupils  to  supply 
them. 


DICTATION.  31 

(5)    Require  pupils  to  give  sentences  with  certain 

homonyms. 
(<?)    Give  sentences  orally,  and  require  children 

to  spell  the  homonyms. 

CAPITALS. 
Steps  in  Method.1 

1.  Recognition  in  reading  matter. 

2.  Mastery  of  rule. 

3.  Application. 

PUNCTUATION. 

Punctuation  is  a  device  for  the  ready  interpreta- 
tion of  written  languages ;  hence,  ability  to  punctuate 
demands  both  a  rational  and  a  formal  process  —  the 
former  corresponding  to  the  mental  process  which  de- 
termines the  separate  groups. of  words,  and  the  latter 
dealing  with  the  kinds  of  punctuation  marks  that 
should  be  inserted. 

PARAGRAPHING. 

Paragraphing,  like  punctuation,  is  a  device  which 
has  a  mechanical  and  a  rational  side  —  the  former  deal- 
ing with  its  printed  form,  and  the  latter  with  the  rela- 
tion which  its  component  sentences  bear  to  itself. 

Fundamentals. 

1.  Necessity  for  punctuation  and  for  paragraphing  is 
determined  by  the  content  of  the  selections ;  hence,  in 

1  Same  for  abbreviations  and  letter  forms. 


32  DICTATION. 

teaching,  emphasis  should  first  be  laid  on  the  content, 
then  on  the  form. 

2.  Since  mastery  of  the  thought  is  a  prerequisite  to 
punctuation  and  to  paragraphing,  the  selections  chosen 
should  be  adapted  to  the  understanding  of  the  pupils. 

3.  Punctuation  and  paragraphing  should  be  learned 
inductively  and  applied  deductively. 

Method. 
The  Period : 

1.  John  is  a  good  bo}r. 

2.  I  have  a  new  book. 

3.  The  tree  has  many  leaves. 

etc.,  etc.,  etc. 

The  child  notices  that  the  first  sentence  ends  in  a  . 
He  notices  that  the  second  sentence  ends  in  a  . 
He  notices  the  .  at  the  end  of  each  subsequent  sentence. 
He  concludes 1  that  each  similar  sentence  must  end 
in  a  . 

THE  PARAGRAPH. 

Form : 

This  knowledge  the  child  obtains  by  having  his  atten- 
tion called  to  the  indention  which  marks  the  beginning 
of  each  paragraph. 

Content : 

Successive  paragraphs  are  read  and  analyzed  into 
their  component  sentences.  Each  group  is  then  shown 
to  deal  with  some  particular  topic  of  the  theme. 

1  By  a  similar  reasoning  he  concludes  that  each  sentence  must 
begin  with  a  capital. 


DICTATION.  35 

Example  : 

"  Once  there  was  a  little  girl  who  had  a  beautiful  red 
hood.  It  was  as  red  as  the  sun  when  it  sets  behind  the 
clouds  in  summer.     Her  grandma  gave  it  to  her. 

"  '  This  is  a  fairy  hood,'  said  her  grandma.  '  It  will 
always  look  just  as  pretty  as  it  does  now.  You  must 
wear  it  every  time  you  go  out.'  " 

Analysis : 
The  topics. 

1.  The  Hood. 

1,  (a)  The  owner  of  the  hood. 
(5)   The  color  of  the  hood. 

(c)   How  the  owner  obtained  the  hood. 

2.  What  Grandma  Said. 

2.  (a)   Of  the  peculiar  attribute  of  the  hood. 

(b)  Of  the  peculiar  virtue  of  the  hood. 

(V)    In  the  shape  of  advice  concerning  the  hood. 
Application : 

(a)  To  reading  matter. 

(F)  To  writing  from  topical  outlines. 

(c)  To  arrangement  of  sentences  into  topics. 
(h  and  c  are  correlated  with  composition.) 

_  USE  OF  DICTIONARY. 

Presupposes : 

1.  A  knowledge  of  the  letters  of  the  alphabet  and 

the  order  of  their  sequence. 

2.  Ability  to  determine  the  proper  word  by  a  refer- 

ence to  the  content. 


36  DICTATION. 

Dictation  as  a  Test. 
(The  Fifth  Herbartian  Step.) 
1.    How  the  Exercise  is  Conducted: 

(a)  At  least  one  child  writes  on  the  blackboard, 
while  the  rest  write  on  paper. 

(5)  The  number  of  words  dictated  consecutively 
depends  upon  the  mental  capacit}7  of  the 
child  and  upon  the  nature  of  the  selection. 

(e)  Only  groups  of  related  words  are  dictated. 

(d)  The  speed  of  the  dictation  is  limited  by  the 

ability  of  the  majority  of  the  class  to  take 
down  the  exercise  verbatim. 

(e)  No  repetition  is  permissible  unless  it  is  de- 

manded by  the  content  of   the  selection. 

Method  of  Correction: 

(a)  Individual  children  are  called  upon  to  read 
their  written  exercises,  the  rest  meanwhile 
inserting  omissions. 

(J)  The  blackboard  exercise  as  "  proof-sheet," 
the  attention  is  directed  first  to  the  para- 
graphs as  wholes,  then  to  the  separate  sen- 
tences as  wholes,  and  lastly  to  the  elements 
of  each  sentence. 

(c)  Classes  that  are  supplied  with  dictionaries 
should  use  these  to  look  up  the  correction 
of  misspelled  words  and  the  meanings  of 
unknown  words. 


o 


DICTATION.  39 

(t?)  Correction  is  made  by  passing  a  line  through 
the  error,  rewriting  correctly  above  the 
word,  and  in  the  case  of  a  misspelled 
word,  writing  it  also  below  the  exercise. 

General  Directions. 

(a)  Time  must  be  assigned  for  the  study  of  the 
corrected  forms,  and  for  recitation  by  sev- 
eral pupils. 
(6)  Each  sheet  of  paper  should  contain  two  origi- 
nal   dictations ;     if    redictation    is    deemed 
advisable,  it  should  be  taken  on  a  separate 
sheet. 
(V)  An  oral  review  of  exercises  should  be  had  at 
least  once  a  month,  when  children  are  given 
an  opportunity  to  restudy  previous  correc- 
tions.    A  recitation  should  follow. 

Model  Lesson.1 
(Report  of  a  lesson  in  a  6 A  grade.) 

The  teacher  dictated  the  following  in  groups  of 
words  included  between  the  vertical  lines : 

As  the  fair  happened  on  the  following  day,  |  I  had 
intentions  of  going  myself.  | 

"  No,  my  dear,"  said  my  wife,  |  "  our  son  Moses  is  a 
discreet  boy,  |  and  can  buy  and  sell  to  very  good  ad- 
vantage." j 

1  The  main  aim  of  the  lesson  was  to  test  the  children's  knowledge 
of  paragraphs  and  quotation  marks. 


40  DICTATION. 

As  I  also  had  a  good  opinion  of  my  son's  pru- 
dence, |  I  was  willing  enough  to  trust  the  business 
with  him.  | 

Method  of  correcting  the  "Proof-sheet." 

Teacher.  How  many  paragraphs  in  this  dicta- 
tion ? 

Pupil.     Three. 

T.     Why  ? 

P.     Assigns  reason. 

T.  How  many  complete  thoughts  in  the  first  para- 
graph ? 

P.     One. 

T.     In  the  second  ? 

P.     One. 

T.     In  the  third  ? 

P.     One. 

T.  Do  you  notice  any  mistakes  in  the  use  of  the 
quotation  marks?  In  the  use  of  any  other  punctua- 
tion marks  ? 

P.     Assigns  reasons  for  corrections. 

T.  Do  you  notice  any  other  mistakes  in  the  first 
sentence  ?  in  the  second  sentence  ?  in  the  third  sen- 
tence ? 

P.     Makes  corrections. 

Each  child  next  corrected  his  own  exercise,  using 
the  blackboard  as  guide,  and  studied  the  correct  forms 
for  a  subsequent  recitation. 


DICTATION.  43 

The  "Proof-sheet." 
As  the  fair  happened  on  the  following  day,  I  had 

intentions  ^f  »» 

intensions  of  going   myself.     "  No,  my  dear,  said  my 

a  discreet  ±. 

wife,  our  son  Moses  is  a  discret  boy  and  can  buy  and 

advantage 

sell  to  very  good  advantag."  rndence 

As  I  also  had  a  good  opinion  of  my  son's  prudense, 
I  was  willing  enough  to  trust  the  business  with  him. 


1. 

intentions 

5. 

discreet 

2. 

H 

6. 

i 

3. 

?> 

7. 

advantage 

4. 

u 

8. 

prudence 

III.  —  COMPOSITION. 

1.  The  arrangement  of  thoughts  in  their  logical  order, 
and 

2.  Their  expression  in  correct  language. 

A  child  has  neither  the  information,  the  reasoning 
power,  nor  the  training  to  write  a  masterly  treatise  ; 
but  under  proper  conditions  he  can  be  furnished  with 
the  information  ;  he  can  be  taught  to  express  it  gram- 
matically ;  and  he  can  be  trained  to  arrange  his  thoughts 
logically.  It  must  be  borne  in  mind,  however,  that  the 
development  of  a  higher  faculty  through  exercise  pre- 
supposes a  particular  exercise  of  a  lower  faculty. 

Fundamentals. 

1.  The  subject-matter  and  the  manner  of  treatment 
should  be  adapted  to  the  child's  interests  and  capacities. 

2.  Oral  composition  should  be  practiced  long  before 
an  attempt  is  made  at  written  composition  —  the  pen- 
manship and  the  spelling  are  obstacles. 

3.  Composition  should  not  be  subordinated  to  other 
studies,  but  should  be  made  an  aim  in  itself. 

4.  The  child's  self-activity  should  be  called  into  play 
at  every  opportunity. 

44 


COMPOSITION.  47 

Kinds  of  Composition : 

1.  Reproduction  of  a  model  (perception). 

2.  Imitation  of  a  model  (imagination). 

3.  Writing  from  topical  outlines  (judgment). 

4.  Wholly  original  (reasoning). 

Method. 
Presentation : 

1.  2.  3.  (a)  Models  read  by  teacher  and  dis- 
cussed (or  subject  and  treatment  discussed  for  2 
and  3). 

(5)  Orally  reproduced  by  several  children. 

(e)  Compositions  written,  and  several  read. 

4.    (a)  Title  written  on  blackboard. 

(b)  Children  volunteer  information,  and  write 
corrected  forms  on  the  blackboard.1 

(<?)  Attention  directed  to  sequence  of  sentences 
and  to  their  division  into  paragraphs,  giv- 
ing to  each  of  the  latter  its  appropriate 
heading. 

(<T)  Only  headings  left  on  blackboard,  and  chil- 
dren called  upon  to  give  oral  expression 
to  the  thoughts. 

(e)  Compositions  written  and  several  read. 

1  This  order  of  presentation  is  changed  as  soon  as  the  ability  of  the 
children  warrants  it,  by  choosing  as  the  initiatory  exercise  the  deter- 
mination of  the  topical  outline  and  the  volunteering  of  information 
by  the  children. 


48  COMPOSITION. 

Correction : 

1.  Compositions  written  on  blackboard. 

2.  Criticised  by  class  (see  Dictation,  Method  of  Cor- 
rection, b  and  dy 

3.  Compositions  rewritten. 

General  Remarks : 

1.  Make  haste  slowly  —  quality  rather  than  quantity. 

2.  The  oral  work  is  the  most  important  part  of  the 
exercise. 

3.  Compositions  are  written  on  blackboard  before 
or  after  the  regular  school  session. 

4.  Home  lessons  may  be  assigned  in  the  upper  grades. 

5.  Other  compositions  besides  those  written  on  the 
blackboard  may  be  criticised,  but  always  in  the  pres- 
ence of  the  child. 

Model  Lessons. 
a.    Reproduction : 

(Report  of  a  lesson  in  a  5B  grade.) 

1.    The  teacher  read  the  following  fable  to  the  class : 

THE   DOG    IN    THE   MANGER. 

There  was  once  a  dog  who  lay  all  day  long  in  a 
manger  where  there  was  plenty  of  hay.  A  horse,  a 
cow,  a  sheep,  and  a  goat  came  one  by  one  and  wanted 
to  eat  the  hay.  The  dog  growled  at  them  and  would 
not  let  them  have  so  much  as  a  mouthful.     Then  an 


COMPOSITION.  51 

ox  came  and   looked  in,  but  the  dog  growled,  at  him 
also. 

"You  selfish  fellow  !  "  said  the  ox,  "you  cannot  eat 
the  hay.  Why  do  you  want  to  keep  it  all  to  your- 
self ?  " 

2.  Several  pupils  were  now  called  upon  to  repro- 
duce the  reading  orally  and,  at  the  conclusion  of  each 
recitation,  the  class  made  the  necessary  corrections.1 

3.  Compositions  were  written. 

4.  After  a  number  of  pupils  had  been  called  upon  to 
read  their  compositions,  which  served  both  as  models 
and  as  subjects  for  criticism,  the  attention  of  the  class 
was  directed  to  the  correction  of  the  "proof-sheet." 

5.  Compositions  that  had  been  criticised  either  by 
the  class  or  by  the  teacher  were  rewritten.2 

(Example  of  a  Child's  Reproduction.) 

THE   DOG    IN   THE   MANGER. 

There  was  once  a  dog  who  lay  all  day  long  in  a 
manger  which  was  full  of  hay.  Soon  a  horse,  a  cow,  a 
sheep,  and  a  goat  came  one  by  one  to  eat  the  hay,  but 
the  dog  growled  at  them  and  would  not  let  them  have 
even  a  mouthful. 

Next,  an  ox  came  to  eat  the  hay  and  the  dog  growled 

1  In  this  instance,  also,  the  teacher,  by  several  well-directed  ques- 
tions, led  the  children  to  recognize  the  number  of  paragraphs  into 
which  the  reading  was  divided  —  another  example  of  correlation. 

2  The  teacher  himself  corrected  about  one  third  of  the  composi- 
tions of  the  class,  in  the  presence  of  individual  pupils. 


52  COMPOSITION. 

at  him  too,  but  the  ox  said,  "  You  foolish  fellow,  you 
cannot  eat  hay.  Why  don't  you  let  somebody  else 
have  it  then?  " 

b.    Imitation: 

(Report  of  a  lesson  in  a  6B  grade.) 

1.  The  teacher  read  the  following  to  the  class : 

THE  CAT,  THE  MONKEY,  AND  THE  CHESTNUTS. 

A  Cat  and  a  Monkey  were  sitting  one  day  by  the 
hearth,  watching  some  chestnuts  which  their  master 
had  laid  down  to  roast.  The  chestnuts  had  begun  to 
burst  with  the  heat,  and  the  Monkey  said  to  the  Cat : 

"  It  is  plain  that  your  paws  were  made  to  pull  out 
those  chestnuts.  Your  paws  are,  indeed,  exactly  like 
our  master's  hands." 

The  Cat  was  greatly  flattered  by  this  speech  and 
reached  forward  for  the  tempting  chestnuts;  but 
scarcely  had  she  touched  the  hot  ashes  than  she  drew 
back  with  a  cry,  for  she  had  burned  her  paw.  She 
tried  again,  and  made  out  to  get  one  chestnut ;  then 
she  pulled  another,  and  a  third,  though  each  time  she 
singed  the  hair  on  her  paws. 

When  she  could  pull  no  more,  she  turned,  and  found 
that  the  monkey  had  taken  this  time  to  crack  the  chest- 
nuts and  eat  them. 

2.  Several  compositions  were  read,  discussed,  and 
criticised. 

3.  4,  5,  same  as  in  a. 


COMPOSITION.  55 

(Example  of  a  Child's  Imitation.) 

THE    GIRL,    THE   BOY,    AND   THE   CANDY. 

One  day,  while  a  little  girl  was  sitting  under  a  tree 
eating  some  candy,  a  boy  came  up  to  her  and  asked  her 
to  get  him  some  water  from  a  spring  near  by.  "  Why 
don't  you  go  yourself?  "  she  asked. 

"  Because  it  will  taste  better  if  you'll  get  it  for  me," 
lie  answered.  This  speech  so  flattered  the  little  girl 
that  she  laid  her  candy  on  the  grass  and  ran  off  to  fetch 
the  water. 

But,  alas !  when  she  returned,  there  was  neither  boy 
nor  candy  to  be  seen.  That  day  she  learned  a  lesson 
she  never  forgot.  It  is  :  "Never  allow  people  to  flatter 
you  into  doing  things  which  they  can  do  for  them- 
selves." 

0.  Topical  outline : 

(Report  of  a  lesson  in  a  7 A  grade.) 

ROBERT   FULTON. 

1.  A  talk  on  the  life  of  Robert  Fulton  by  the  teacher, 
and  an  oral  reproduction  by  the  children. 

2.  The  following  topics  were  written  on  the  black- 
board by  the  teacher : 

(a)    Robert  Fulton  at  home  and  at  school. 
(b~)    A  youthful  invention. 

(<?)    His  greatest  and  most  successful  invention, 
(c?)   His  death. 

3.  4,  and  5  same  as  in  a. 


56  COMPOSITION. 

(Example  of  a  Child's  Composition.) 

ROBERT   FULTON. 

Robert  Fulton  was  born  in  1765,  in  Little  Britain, 
Pa.  When  he  was  three  years  old,  his  father  died,  and 
his  mother  was  left  to  take  care  of  his  education.  She 
taught  him  until  he  was  eight  years  old.  He  did  not 
have  a  great  liking  for  books.  He  was  very  much 
interested  in  mechanical  drawing. 

Robert  came  late  to  school  one  day.  After  being 
reproved  by  the  schoolmaster,  he  said,  "  I  was  at  a  shop, 
hammering  a  piece  of  lead  into  a  pencil."  Soon  after, 
the  children  were  using  the  same  kind  of  pencils. 

Fulton  invented  the  first  steamboat.  He  called  it 
the  Clermont,  after  his  friend  Livingston's  home  on  the 
Hudson.  Its  first  trip  took  place  in  1807.  It  started 
from  New  York  and  sailed  up  the  Hudson  River  to 
Albany,  which  was  a  distance  of  one  hundred  and  fifty 
miles.  It  took  her  thirty-two  hours  to  make  this  trip. 
People  stood  along  the  banks  of  the  Hudson  River,  say- 
ing they  didn't  think  the  boat  would  go.  They  called 
it  "Fulton's  Folly."  They  were  very  much  surprised 
when  they  saw  the  boat  begin  to  move. 

Robert  Fulton  died  in  1815.  The  world  owes  a 
great  deal  to  this  man. 

d.     Original : 

(Report  of  a  lesson  in  an  8 A  grade.) 
1.    The  pupils,  under  the  supervision  of  the  teacher, 


COMPOSITION.  59 

determined  upon  the  following  headings,  without  in- 
sisting upon  the  order  of  their  treatment : 

(a)  What  food  does. 

(5)  Kinds, 

(c)  Preparation, 

(c?)  Necessity. 

(e)  Dangers. 

2.  The  pupils  volunteered  a  number  of  sentences, 
each  of  which,  in  turn,  was  first  examined  for  its  syn- 
tax, and,  if  approved,  was  written  on  the  blackboard 
and  examined  for  written  mistakes.  It  was  then 
assigned  to  its  proper  heading. 

Sentences  Volunteered. 

(a)    Food  builds  up  the  body. 

Our   bodies   are    constantly   wearing   away, 
therefore   we   must   have   food   to   repair 
them. 
Pure  food  gives  pure  blood. 
(Z»)    There  are  three  kinds  of  food,  animal,  vege- 
table, and  mineral. 
Air  is  a  food. 

Some  parts  of  the  body  need  special  food,  as, 
for  instance,  the  brain  needs  phosphorus, 
and  the  bones  need  lime. 
(o)    All  food  should  be  well  chewed  before  it  is 
swallowed,  or  it  will  cause  indigestion. 
We  cook  food  to  help  digestion. 


60  COMPOSITION. 

(t?)    If  you  do  not  get  enough  food,  your  body 
will  become  weakened. 
We  must  eat  pure  food  in  order  to  be  healthy. 
Man  cannot  live  on  one  kind  of  food,  but  must 
have  several  kinds  mixed  in  right  propor- 
tion, 
(e)     There  are  some  things  we  must  avoid,  such  as 
tobacco,  drugs,  and    liquor,  for    they  are 
poisonous. 
Liquor  is  dangerous  to  the  body  because  it 

contains  alcohol. 
We  must  exercise  the  muscles  in  order  to  get 
food  from  the  blood.1 

3.  Everything  but  the  headings  was  erased  from  the 
blackboard ;  and  after  several  pupils  had  reproduced 
the  subject  orally,  the  class  wrote  the  composition. 

4  and  5  same  as  in  a. 

1  It  need  surprise  no  one  to  learn  that  the  pupils  did  not  give  the 
sentences  in  the  exact  order  given  above.  However,  they  made  a 
laudable  attempt  to  confine  their  attention  to  a  single  heading  at  a 
time  —  a  practice  which,  if  repeated  sufficiently  often,  will  tend  to  form 
a  habit  of  concentrated  thinking  in  composition  writing. 


IV.  —  GRAMMAR. 

Aims : 

1.  Intellectual  discipline. 

2.  Knowledge. 

Grammar  deals  with  certain  phases  of  the  content 
and  the  form  of  the  sentence.  It  treats  (a)  of  the 
relations  and  the  functions  of  the  thought-elements,  and 
(5)  it  presents  certain  forms  of  expression  which  usage 
has  imposed  upon  our  language.  The  standard  of  the 
one  is  in  the  mind,  hence  universal  and  unchangeable ; 
the  standard  of  the  other  is  in  custom,  and  hence  sub- 
ject to  change.  Analysis,  which  concerns  itself  with 
content,  belongs  to  the  former;  syntax  belongs  to  the 
latter.  Briefly  stated,  grammar  on  its  rational  side  is 
the  psychology  of  the  sentence ;  on  its  formal  side  it  is 
a  guide  to  correct  usage. 

Fundamentals. 

1.  The  sentence  is  the  basis  of  the  study  of  gram- 
mar. 

2.  The  analysis  of  a  sentence  into  its  elements  pre- 
supposes : 

63 


64  GRAMMAR. 

(a)    A  clear  understanding  of  the  thought  con- 
veyed. 
(5)    A  sufficient  degree  of  mental  development. 

3.  Like  all  studies  that  yield  to  scientific  treatment, 
grammar  should  be  taught  inductively  and  applied 
deductively. 

Method. 

Aim  :   The  concept,  Sentence. 

Place  on  blackboard  a  series  of  unrelated  words ;  as, 
this,  told,  birds,  farm,  a,  lived,  stoiy,  fly,  Franklin,  boy, 
on ;  then  direct  your  pupils'  attention  to  a  comparison 
of  these  with  their  rearrangement  into  the  combina- 
tions :  birds  fly,  the  boy  lived  on  a  farm,  Franklin  told 
this  story,  etc. 

Generalization  (naming)  and  application  should  fol- 
low in  this  as  in  subsequent  lessons. 

Aim :  Analysis  of  the  Simple  Sentence. 

1.  The  sun  |  shines. 

2.  The  boy  |  lived  on  a  farm. 

3.  Franklin  |  told  this  story. 


is  the  capital  of  Massachu- 
setts. 


4.  The  city  of  Boston 

5.  Exercise  |  must  be  taken  daily. 


GRAMMAR. 


07 


By  means  of  questions  lead  your  pupils  to  recognize 
the  two  coordinate  elements  of  each  sentence,  as  fol- 
lows : 


Questions  by  teacher. 

1.  What  shines? 

What  does  the  sun  do? 
What  is   said  concern- 
ing the  sun? 

2.  Who  lived  on  a  farm  ? 
What  about  the  boy  ? 

3.  Who  told  this  story? 
What  did  Franklin  do, 

or  what  does  this  sen- 
tence tell  you  con- 
cerning Franklin? 

4.  What  is  the  capital  of 

Massachusetts  ? 
What  is  said  of  the  city 
of  Boston? 

5.  What    must    be    taken 

daily  ? 
What  concerning  exer- 
cise? 


Answers  by  pupils. 
The  sun 


shines. 

The  boy 

lived  on  a  farm. 

Franklin 


told  this  story. 
The  city  of  Boston 

is   the    capital    of    Massa- 
chusetts. 

Exercise 


must  be  taken  daily. 


By  comparison,  the  idea  is  now  brought  prominently 
to  the  pupils'  attention  that  the  sentence  concerns  itself 
with  something  of  which  the  rest  of  the  sentence  treats. 


68  GRAMMAR. 

That  "  something  "  is  the  subject ;  what  is  stated  con- 
cerning the  subject  is  the  predicate.1 

Aim  :   The  concept,  Complex  Sentence. 

1.    A.    I  was  thus  employed. 

B.    The  enemy  discharged  several  thousand  ar- 
rows. 
We  have  here  two  simple  sentences  which  give  no 
evidence  of  connection  or  of  relationship. 

C.  While  I  was  thus  employed,  the  enemy  discharged 
several  thousand  arrows. 

By  skillful  questioning,  the  pupil  can  be  led  to  per- 
ceive : 

1.  That  the  two  statements  have  been  incorporated 
into  one  (clauses). 

2.  That  the  two  statements  are  now  not  only  con- 
nected but  related  —  A  being  the  occasion  of  B  (de- 
pendence). 

3.  That  A  relates  to  "discharged"  (adverbial). 

These  ideas  must  now  be  mastered ;  and  this  is  done 
by  (a)  repetition,  (6)  type-sentence. 

The  type-sentence  is  of  value  both  as  the  repository 

1  The  difficulty  children  encounter  in  discovering  the  elements  of  a 
sentence  is  due  largely  to  the  neglect  to  emphasize  the  dependence  of 
these  elements  upon  each  other.  To  obviate  this  difficulty,  the  child 
should  be  trained  to  think  of  the  subject-predicate,  and  of  predicate- 
subject  and  to  recite  the  subject  and  predicate  together,  laying  empha- 
sis upon  the  particular  element  called  for  in  the  answer.  Thus  in  the 
sentence,  "Birds  fly,"  if  the  subject  is  asked  for,  the  child  recites, 
"Birds  [fly]  "  ;  if  the  predicate,  "  [Birds]  fly." 


GRAMMAR.  71 

of  the  ideas  and  as  the  concrete  standard  with  which  to 
compare  similar  sentences.  Hence,  every  new  concept 
should  have  a  type  as  its  accompaniment. 

Repetition  is  essential  to  stamp  knowledge  upon  the 
mind — not  the  kind  of  repetition  that  degenerates  into 
a  mechanical  process,  but  the  one  that  calls  to  its  assist- 
ance variety,  interest,  and  thought.  In  conformity 
with  this,  the  following  method  is  suggested  for  the 
study  of  the  type-sentence :  Having  induced  the  prin- 
ciple, the  pupils,  while  applying  it  to  a  variety  of  sen- 
tences, should  be  called  upon  at  frequent  intervals  to 
apply  it  to  the  type-sentence,  until  they  are  able  to 
recall  readily  the  sentence  and  the  process. 

Model  lesson  to  determine  the  structural  character  of  a 
sentence. 

To  determine  the  structural  character  of  a  sentence, 
we  need  to  know : 

1.  The  number  of  clauses  composing  it. 

2.  The  nature  of  the  relationship  existing  between 
these  clauses. 

Model. 

What  kind  of  a  sentence  is  the  following? 

"  Accordingly,  when  he  came  to  the  convention  in 
Independence  Hall  as  a  delegate  from  Virginia,  he 
chose  a  good  seat  where  he  could  hear  all  that  was 
said." 

First  Step:  to  determine  the  number  of  clauses. 


72  GRAMMAR. 

1.  (Accordingly)  he  chose  seat. 

2.  (when)   he  came  Virginia. 

3.  (where)  he  could  hear  all. 

4.  (that)  was  said. 

The  idea  of  the  simple  sentence  is  now  eliminated. 

Second  Step:  to  determine  the  dependence  or  inde- 
pendence of  the  clauses. 

1.  independent  clause. 

2.  relates  to  "  chose  "  ;  dependent  clause. 

3.  relates  to  "  chose  "  ;  dependent  clause. 

4.  relates  to  "  all  "  ;  dependent  clause. 

Third  Step  :   Conclusion  :   Complex  Sentence. 

The  Diagram. 

As  a  graphic  representation,  it  is  of  great  value,  espe- 
cially for  beginners,  and  should  be  employed  for  both 
analysis  and  synthesis  of  each  sentence. 

The  Parts  of  Speech. 

Should  be  taught  inductively  through  the  medium 
of  the  sentence,  with  the  Formal  Steps  for  guides. 

Parsing. 
Process:  deduction. 

Warning:  do  not  invert  the  order  of  the  deductive 

process  —  major  premise,  minor  premise,  conclusion. 

Examples  of  parsing : 
John  bought  a  new  book. 
1.    Parse  "new." 


GRAMMAR.  75 

Major  premise  (adjectives  are  words  which  modify 
nouns  or  pronouns).  Children  are  credited  with  this 
knowledge,  and  are  not  called  upon  to  repeat  it. 

Minor  premise:   "new"  describes  "book." 

Conclusion:  "new"  is  an  adjective. 

Briefly:  "  new  "  describes  "  book  "  and  is  an  adjective. 

2.    Parse  "John." 

Proper  noun subject  of  "bought,"  and 

is  in  the  nominative  case. 

False  Syntax. 

The  recitations  and  the  compositions  of  the  pupils 
should  furnish  material  for  the  correction  of  sentences. 


V.  — LITERATURE. 

A  masterpiece  of  literature  may  be  studied  for  com- 
prehension, or  read  for  appreciation,  or  analyzed  for 
criticism.1  This  must  be  borne  in  mind  in  discussing 
the  subject  of  method  in  literature. 

Fundamentals. 

1.  As  the  aim  determines  the  mental  processes  en- 
gaged in  its  attainment,  it  also  determines  the  method. 

2.  As  comprehension  must  precede  appreciation, 
and  appreciation  must  precede  criticism,  the  mental 
processes  engaged  in  executing  these  aims  bear  to 
each  other  the  relation  of  the  simple  to  the  complex. 
Hence  the  method  for  appreciation  includes  that  for 
comprehension,  and  the  method  for  criticism  includes 
that  for  appreciation.2 

1  Criticism  is  beyond  the  province  of  the  elementary  schools,  and 
will  not  be  discussed  here. 

2  The  opinion  expressed  by  certain  optimistic  theorists  that  a  child 
can  appreciate  literature  that  he  does  not  comprehend  is  about  as 
sound  as  would  be  the  claim  that  he  can  criticise  a  selection  he  does 
not  appreciate.  As  a  matter  of  fact,  the  child  who  finds  pleasure  in 
listening  to  the  reading  of  a  passage  he  does  not  understand  does  so, 
not  because  he  appreciates  the  literature  as  such,  but  because  he  is 
attracted  by  its  delivery.  This  view  is  not  poetic,  but  neither  are  a 
great  many  other  truths. 

76 


LITERATURE.  79 

3.  Comprehension  presupposes  a  knowledge  of  the 
intellectual  elements  of  the  composition,  and  of  their 
relations. 

4.  Appreciation  demands,  as  conditions  to  success: 

(a)  Intellectual  mastery  of  the  exercise. 
(5)  Feelings  sufficiently  developed  to  apperceive 
the  sentiments  conveyed  in  the  selection. 

(c)  The    imagination    awakened    to    the    proper 

degree  of  activity. 

(d)  An  attractive  presentation. 

Conclusion:  As  appreciation  is  the  aim  of  this  study 
in  the  elementary  schools,  a  masterpiece  will  call  for 
either  one  reading  or  two.  If  the  selection  is  one 
which  presents  no  difficulty  to  the  understanding  of 
the  child,  one  reading,  and  that  for  appreciation,  is  all 
that  is  essential ;  otherwise,  two  readings  will  be  found 
necessary  —  the  first  for  intellectual  mastery,  and  the 
second  for  appreciation. 

Method. 
Preparation.     This  will  include  : 

(a)  The  name  of  the  author  and  as  much  of  his 
life's  history  as  is  warranted  by  the  selection.  Culture 
demands  this. 

(5)  The  occasion  of  the  masterpiece.  This  gives  the 
proper  background  and  atmosphere  to  the  thoughts  and 
sentiments  of  the  author,  and  paves  the  way  to  a  proper 
apperception.     For  example,  in  order  that  a  child  may 


80  LITERATURE. 

appreciate  the  reading  of  "  Old  Ironsides,"  be  must  first 
become  acquainted  with  the  motive  which  actuated  the 
author  to  write  this  stirring  appeal. 

Presentation. 

(a)  Comprehension.  When  a  pupil  has  read  through 
a  paragraph  carefully  and  has  failed  to  grasp  its  mean- 
ing, he  should  search  out  the  cause  or  causes  of  his  fail- 
ure and  proceed  to  remove  them  by  a  study  of  : 

1.  The  meanings  of  unknown  words.  The  individ- 
ual members  of  the  class,  the  dictionary,  the  teacher, 
and,  on  rarer  occasions,  the  content,  may  each  become 
the  source  of  information. 

2.  Figures  of  speech.  These  variations  of  the  ordi- 
nary mode  of  expression  serve  a  most  important  pur- 
pose in  literature.  They  add  grace  and  refinement  to 
thought  ;  they  clarify  it  ;  they  invest  it  with  new 
charms  ;  they  endow  it  with  greater  vigor  and  power. 
They  therefore  demand  a  proper  share  of  the  child's 
attention  as  living  and  vital  forces  of  our  language. 

3.  Allusions.  These  should  be  regarded  in  the  same 
light  as  are  unknown  words  whose  meanings  are  sought. 
That  is,  their  study  should  not  go  beyond  what  is  neces- 
sary for  a  clear  comprehension  of  them.  To  do  more 
than  this  tends  to  introduce  breaks  in  the  continuity  of 
the  lesson.      Brevity  is  the  soul  of  an  allusion. 

4.  The  grammatical  construction.  The  words, 
phrases,  and  clauses  of  each  sentence  must  be  grasped 
in  their   true   relations   before   the  exact  meaning  of 


LITERATURE.  83 

the  author  can  be  known.  Hence,  grammar  is  called 
upon  at  this  stage  to  complete  and  to  insure  thorough 
comprehension.  The  extent  to  which  grammar  should 
be  utilized  in  the  study  of  a  masterpiece  of  literature 
must  be  measured  by  the  need  of  it  for  a  clearer  under- 
standing of  any  portion  of  the  selection.  Its  use  must 
be  limited  by  the  consideration  that  it  is  of  value  here 
only  in  so  far  as  it  aids  the  child  to  discover  and  to 
strengthen  the  weak  points  in  his  knowledge.1 

(6)  Appreciation.2  While  the  dictionary,  the  rheto- 
ric, the  reference  book,  and  the  grammar,  when  com- 
bined, present  a  complete  array  of  means  for  mastering 
any  suitable  selection,  they  cannot,  unaided,  awaken  and 
develop  appreciation.  This  can  be  brought  about  only 
by  the  teacher  who  is  gifted  with  appreciation,  power, 
and  insight.  Here  method  concerns  itself  less  with 
specific  directions  for  the  conduct  of  the  lesson,  than 
with  the  inquiry  into  the  qualifications  which  a  teacher 

1  The  question  of  an  immediate  rereading  of  each  paragraph  that 
has  been  studied,  and  of  the  final  reading  of  the  whole  selection  for  a 
general  intellectual  survey,  can  be  answered  only  by  the  teacher,  who 
is  guided  by  the  varying  conditions  which  confront  him. 

2  The  appreciative  reading  of  a  masterpiece  need  not  follow  imme- 
diately upon  the  completion  of  its  study.  Indeed,  the  opinion  is  ventured 
that  better  results  will  follow  if  several  months  are  allowed  to  intervene 
before  entering  upon  the  appreciative  reading  of  a  selection  that  had 
previously  been  read  for  comprehension.  In  this  connection,  the  plan 
is  suggested  of  assigning  to  each  grade  two  classes  of  masterpieces,  — 
one,  easily  comprehended,  for  appreciative  reading  ;  the  other,  of  oppo- 
site character,  for  thorough  study.  The  latter  may  then  be  read  for 
appreciation  during  some  subsequent  term. 


84  LITERATURE. 

must  possess,  or  must  strive  to  acquire,  if  possible,  in 
order  that  he  may  inculcate  in  the  child  a  desire  for 
good  literature. 

A  teacher  who  is  himself  a  lover  of  good  literature 
cannot  fail  to  communicate  more  or  less  of  this  feel- 
ing to  his  pupils  ;  for,  "  Love  beams  from  the  eye, 
glides  from  the  tongue,  and  finds  its  echo  in  some 
heart." 

A  teacher  who  combines  oratorical  powers  with  his 
love  for  literature  not  only  awakens  and  maintains 
the  interest  of  the  pupils  in  any  particular  selection, 
but  also  instills  in  them  a  desire  to  become  acquainted 
with  other  selections. 

And,  finally,  if,  in  addition  to  his  other  qualifications, 
the  teacher  possesses  teaching  tact,  —  if  he  knows  how 
to  adapt  his  instruction  to  the  child's  apperception,  in- 
terest, and  imagination,  —  he  can  best  attain  the  aim 
of  this  study  by  merely  reading  the  selection  to  the 
class,  and  by  insinuating  information,  comment,  or  pre- 
cept, —  in  short,  whatever  his  native  or  acquired  tact 
may  suggest. 


VI.  — NATURE   STUDY. 

Aims : 

1.  To  inculcate  a  feeling  of  sympathy  for  nature. 

2.  To  learn  nature's  laws  and  their  application. 

This  study  is  a  composite  of  a  number  of  sciences 
which  fall  under  the  two  general  divisions  of  observa- 
tional and  experimental  science.  To  the  former  belong 
botany,  geology,  zoology,  meteorology,  and  astronomy  ; 
to  the  latter  belong  physics  and  chemistry. 

Early  man  spent  a  large  part  of  his  time  in  studying 
the  observational  sciences.  He  was  interested  in  the 
plants,  in  the  soil,  in  the  animals,  in  the  weather,  and 
in  the  climate,  for  a  very  obvious  reason  —  the  knowl- 
edge was  essential  to  the  maintenance  of  his  life.  As 
he  advanced  in  civilization,  he  devoted  a  gradually  in- 
creased share  of  his  attention  to  physics  and  chemistry, 
no  longer  for  the  purpose  of  preserving  his  life,  but  to 
economize  effort. 

The  culture  epoch  theory,  if  followed  implicitly, 
would  necessitate  the  study  of  all  the  material  which 
interested  man  in  his  natural  state,  without  taking  into 
account  the  changed  conditions  which  confront  the 
student  of  to-day.  This  is  a  fallacy  into  which  the 
overzealous  advocates  of  nature  study  have  fallen.     If 

87 


88  NATURE   STUDY. 

a  city  child,  because  of  his  innate  love  for  the  beautiful, 
is  interested  in  flowers,  does  it  follow  that  he  will  be 
interested  in  the  snake  simply  because  some  forefather 
of  his  in  the  remote  ages  needed  that  knowledge  for  his 
personal  safety  ?  If  natural  phenomena  appeal  to  the 
child,  will  the  knowledge  of  cecropia,  polyphemus,  or 
cynthia  have  the  same  effect  ?  What  possible  reason, 
utilitarian,  intellectual,  aesthetic,  or  ethical,  is  there  for 
burdening  the  child's  mind  with  knowledge  of  spiders, 
slugs,  toads,  and  bats  ? 

A  little  of  everything  and  not  much  of  anything  is 
the  motto  carried  out  to  an  extent  little  dreamed  of 
even  by  Comenius.  Not  only  is  this  study  made  to 
include  seven  sciences,  not  to  mention  the  sciences 
which  are  directly  or  indirectly,  logically  or  psycho- 
logically, sensibly  or  nonsensically,  correlated  with  it, 
but  each  science  is  loaded  down  with  an  overwhelming 
amount  of  material,  some  of  which  is  uninteresting  to 
the  child,  some  is  unessential,  and  some  is  suitable  only 
for  the  specialist.  If  observational  science  is  confined 
to  that  portion  of  earth  study  and  of  natural  phenomena 
that  is  essentially  a  preparation  to  the  study  of  geogra- 
phy, and  if  a  little  botany  is  added  'to  it,  the  child  has 
all  he  can  cover  without  skimming  during  the  first  few 
years  of  his  school  course. 

Fundamentals. 

1.  Observational  science  should  precede  the  experi- 
mental science. 


7 


NATURE   STUDY.  91 

2.  Observation  should  be  regarded  as  a  preliminary 
step  to  the  conception  of  the  causal  idea. 

3.  Basic  considerations  in  the  choice  of  material  : 
the  useful,  the  beautiful,  the  true. 

4.  Observation,  as  well  as  experiment,  should  be 
directed,  ajJf  preferably,  to  material  with  which  the 
child  is  aWeady  familiar. 

5.  Obwvation  and  experiment  should  be  accurate 
in  order  f  lead  to  good  intellectual  habits. 

Method. 

Observation  should  place  the  child  in  direct  contact 
with  the  object  or  phenomenon  to  be  observed.  **&.  child 
can  get  a  clear  idea  of  a  plant  only  by  seeing,  torching, 
smelling,  and  perhaps  tasting  it.  A  picture  gives  him 
only  its  form  and  color,  while  a  verbal  descriptioatgives 
him  —  a  lot  of  words.  Again,  a  prince  of  India  denied 
the  existence  of  water  in  solid  form,  and  no  amount  of 
persuasion  convinced  him.  He  needed  to  be  brought 
face  to  face  with  the  phenomenon. 

From  observation  the  child  passes  to  experiment, 
which  is  the  more  complex  process  and  includes  the 
former.  Here  the  teacher  must  be  guided  by  the 
maxim  to  have  the  child  make  his  own  inductions  and 
deductions. 

Example  of  induction  ; 

The  child  is  given  a  ruler,  a  fulcrum,  and  several 
equal  weights.     He  places  a  weight  on  each  end  of  the 


92  NATURE   STUDY. 

ruler,  which  he  balances  on  the  fulcrum.  He  moves 
one  weight  nearer  the  fulcrum  and  he  finds  that  he 
must  increase  the  power-distance  or  the  weight  in  order 
to  preserve  the  balance.  After  several  observations  of 
like  character,  he  concludes  that  P  x  Pd=  Wx  Wd,  a 
discovery  which  he  proceeds  to  apply. 


VII.  —  GEOGRAPHY. 

Aims: 

1.  Reverence. 

2.  Liber al-mindedness. 

A  characteristic  of  modern  education  is  that  it  aims 
at  the  harmonious  development  of  the  threefold  nature 
of  man  —  physical,  mental,  and  moral.  Another  of  its 
characteristics  is  that,  while  it  conceives  it  possible  to 
exercise  the  mental  powers  through  the  study  of  one 
group  of  subjects,  it  insists  that  certain  studies  are 
inherently  fitted  for  particular  mental  processes.  In 
accordance  with  this  decision,  it  has  assigned  nature 
study  to  the  elementary  school  primarily  for  observa- 
tion, reading  for  imagination,  arithmetic  and  grammar 
for  reasoning,  history  for  prudential  morality,  and 
geography  for  its  highest  aim,  reverence  and  liberal- 
mindedness.  Geography,  properly  taught,  yields  the 
material  which,  if  elaborated  in  accordance  with  the 
mind's  laws,  make   possible    the    attainment    of   these 

aims. 

Fundamentals.1 

I.    The  conditions  to  reverence  are  : 

1.    (a)  A  knowledge  of  the  earth  as  the  dwelling- 
place  of  man  (utilitarian). 
(b)   A  knowledge  of  the  natural  forces  that 
are  at  work  upon  it  (utilitarian). 

1  Read,  in  this  connection,  Fundamentals  under  History. 

95 


96  GEOGRAPHY. 

2.  A  knowledge  of  the  relation  between  the  earth 

and  the  natural  forces  (rational). 

3.  (a)  Contemplation  of  the  earth  beautiful  (aes- 

thetic), and 
(J)   Contemplation  of  causes  and  effects,  lead- 
ing up  to  the  conception  of  the  Uni- 
versal Cause  (ethical). 

II.    The  conditions  to  liberal-mindedness  are  : 

1.  (a)   A  knowledge  of  the  physical  characteris- 

tics of  other  lands. 
(b)   A  knowledge  of  their  inhabitants. 

2.  A  knowledge  of  the  influence  that  habitation 

has  upon  man. 

3.  An   appreciation   of    the   truth    that  we    are 

largely   the    product    of    our    environ- 
ments. 

General  Considerations. 

1.  The  map  represents  the  world  which  the  child 
travels  in  imagination.  Before  he  can  avail  himself  of 
its  services,  however,  he  must  master : 

(a)  The  elementary  notions  of  geography. 
(b~)   The  manner  of  representing  and  of  interpret- 
ing these  notions. 

2.  Elementary  geographical  notions  should  result 
from  observation  or  experience. 

3.  Induction  is  the  proper  method  for  the  teaching 
of  geography. 


GEOGRAPHY.  99 

4.  Ability  to  interpret  the  map  rationally  is  of 
greater  importance  to  the  child  than  the  memorizing  of 
the  numerous  facts  it  contains. 

5.  After  the  child  has  mastered  the  elementary  no- 
tions of  geography,  it  matters  little  to  him  whether  the 
first  topic  presented  for  study  is  the  whole  earth  or  the 
city  or  state  in  which  he  resides,  because,  in  reality, 
they  differ  in  nothing  except  in  size  —  a  concept  which 
a  child  can  grasp  or  disregard  as  readily  as  an  adult  in 
map  study.  What  is  of  importance  to  him,  however,  is 
that  the  topic  is  presented  to  him  in  bold  outlines  and 
subsequently  filled  in. 

Method. 
Elementary  notions : 

Where  direct  observation  of  surface  conditions  is  im- 
possible, clay  or  sand  modeling  should  be  resorted  to. 
A  child  who  has  never  seen  a  lake  can  get  a  pretty 
clear  idea  of  it  by  this  means,  especially  if  the  lesson  is 
supplemented  by  pictures  and  by  a  comparison  with 
some  known  object  for  the  purpose  of  learning  its  size. 

Map  interpretation : 

Have  children  draw  a  large  object,  as  a  blackboard, 
and  call  their  attention  to  the  scale ;  next,  draw  an 
object  to  an  exact  scale.  Represent  objects  in  the  room 
on  the  plane;  later,  represent  a  river,  a  mountain,  etc., 
from  a  clay  model.  Teach  the  cardinal  points  by 
means  of  the  sun,  and  fix  them  on  paper.  Ask  for 
exact  location  of  any  point ;  then  teach  latitude  and 
longitude. 


100  GEOGRAPHY. 

Causal  relations  : 

Geography  is  not  a  compendium  of  isolated  facts  con- 
cerning our  earth,  but  it  is  a  study  which  regards  its 
facts  and  phenomena  as  links  in  a  long  chain  of  causes 
and  effects.  As  an  example,  the  child,  starting  with 
location  and  surface  as  primary  geographical  facts,  is 
led  to  perceive  that  they  are  the  chief  causes  of  cli- 
mate ;  that  location  and  climate  influence  the  life  of 
plant  and  animal,  which  in  turn  influence  man's  occu- 
pation, and  these  in  turn  affect  commerce,  travel,  and 
communication. 

Indeed,  there  is  no  geographical  fact  which  will  not 
yield  to  the  same  treatment.  The  general  surface  of  a 
continent ;  its  mountains,  rivers,  etc.  ;  its  climate  ;  its 
population  ;  the  size  and  location  of  its  cities  ;  the  char- 
acteristics and  governments  of  its  people  ;  its  occupa- 
tions and  productions  ;  its  commerce,  —  each  of  these 
topics  can  be  and  should  be  treated  in  its  causal  relation. 

Ethical : 

i 

Only  he  who  feels  beauty,  sympathy,  and  reverence, 
and  approaches  the  child  with  gentle  tact,  can  awaken 
the  aesthetic  feelings  through  the  contemplation  of 
nature  or  of  nature's  offspring  —  rhythmic  language; 
can  arouse  sympathy  through  the  broadening  of  the 
intellect ;  and  can  transform  rational  insight  into  rev- 
erence. 


VIII.  —  HISTORY. 

Aims : 

1.  Intellectual. 

2.  Ethical. 

History  is  the  biography  of  man.  It  not  only  records 
events  which  have  a  bearing  upon  his  social  life,  but 
searches  out  their  causes  and  effects.  Such  a  concep- 
tion of  the  province  of  history  is  certainly  beyond  the 
mental  grasp  of  the  young  child ;  hence,  the  unfold- 
ing of  the  subject  must  be  made  to  correspond  to  the 
development  of  his  mental  faculties. 

Fundamentals.1 

I.  There  are  three  stages  in  the  development  of  the 
historical  sense  in  children  : 

1.    Narrative. 

(&)  Biography. 
(7>)   Events. 

(a)  Sound  practice  demands  the  recognition  that  chil- 
dren's interests  are  most  readily  awakened  by  concrete 
examples.  Hence,  biography  is  chosen  as  the  intro- 
duction to  narrative  which  has  for  its  basis  events. 

1  Read  also  Fundamentals  under  Geography. 
103 


104  HISTORY. 

(5)  The  transition  to  events  is  natural,  having  been 
accomplished  in  accordance  with  the  laws  governing 
the  acquisition  of  knowledge ;  while  the  new  material 
for  study  takes  into  account  the  child's  increased  men- 
tal development,  particularly  his  imagination. 

2.  Causal. 

(a)  Events. 
(£)   Institutions. 

(a)  Perception  of  causality  is  a  more  difficult  process 
than  perception  of  events,  and  requires  a  higher  degree 
of  mental  development.  The  fall  of  Constantinople 
and  the  discovery  of  America  are  historical  events  which 
any  ordinary  child  can  grasp  ;  but  to  trace  out  the  rela- 
tionship of  cause  and  effect  between  them  is  well  cal- 
culated to  exercise,  not  merely  his  imagination,  but  his 
judgment  and  his  reason  as  well. 

(6)  Institutions,  the  monuments  of  the  world's  prog- 
ress, are  a  fitting  climax  in  the  study  of  history.  But 
whether  they  should  be  dealt  with  as  mere  facts,  or  as 
the  embodiments  of  long  series  of  causes,  is  an  open 
question,  which  can  be  determined  only  by  the  ability 
of  the  pupils  to  master  the  higher  conception. 

3.  Ethical. 

History  is  replete  with  ethical  content  which  the 
teacher  should  avail  himself  of  as  means  for  the  moral 
uplifting  of  the  child.  This  is  the  chief  aim  of  history 
teaching  —  not  to  satisfy  a  craving  for  gossip;  not  to 


HISTORY.  107 

exercise  the  intellectual  faculties ;  but  to  instill  a  habit 
of  right  conduct  through  emulation,  and  a  love  of  coun- 
try through  appreciation  of  others'  sacrifices  and  one's 
own  duties  and  responsibilities. 

II.  The  idea  of  concentric  circles  aptly  characterizes 
the  nature  of  the  relation  which  exists  among  the  mate- 
rials for  historical  study  outlined  above.  They  are 
not  mutually  exclusive ;  on  the  contrary,  they  either 
partly  or  wholly  include  one  another.  Biography  deals 
with  events,  with  cause  and  effect,  refers  to  institutions, 
and  insinuates  ethical  concepts,  even  while  it  lays  stress 
upon  the  individual;  events  are  not  isolated  phenom- 
ena ;  institutions  are  not  purposeless ;  nor  are  ethical 
principles  self-creative. 

Method. 

I.    Biography  and  Events. 

We  become  interested  in  historical  characters  or 
events,  either  when  they  coincide  with  our  sentiments, 
or  when  they  are  viewed  in  their  original  environments. 
We  become  still  more  interested  in  them  when  both 
these  conditions  are  realized. 

The  teacher  of  biography  and  of  narrative,  then, 
must  search  out  all  the  causes  which  have  been  instru- 
mental in  giving  the  subject  of  the  child's  study  a  place 
in  history,  and  then  arrange  the  facts  in  proper  per- 
spective. With  the  plan  of  the  lesson  clear  in  his 
mind,  he  makes  his  presentation,  guided  by  the  thought 
that  the  nearer  biography  and  narrative  approximate 


108  HISTORY. 

actual  occurrences,  the  more  lifelike  the  characters  and 
the  events  are,  the  greater  is  the  appeal  to  the  intellect 
and  to  the  feelings  of  the  listener. 

But  knowledge  alone  will  not  suffice  the  successful 
teacher;  but  back  of  it,  interwoven  with  it,  impelling 
it,  must  be  enthusiasm  —  interest  which  has  gathered  a 
large  amount  of  momentum.  For  it  is  the  enthusiast 
only  who  can  awaken  in  others  feelings  akin  to  his  own. 
Such  interest  on  the  part  of  the  teacher  comes  only 
with  perfect  mastery  of  the  subject.  Deep,  earnest, 
and  frequent  study  is  essential  to  success  in  teaching 
history. 

Minor  points  : 

1.  Mechanical  aids,  such  as  pictures,  portraits,  maps 
—  everything  that  conduces  to  a  reconstruction  of  the 
environment  —  should  be  employed. 

2.  Each  biography  should  represent  an  epoch. 

3.  Before  assigning  a  lesson  for  home  study,  it 
should  be  carefully  explained  by  the  teacher. 

4.  Before  presenting  a  new  lesson,  the  preceding 
lesson  should  be  reviewed  in  order  to  connect  the 
events  hi  the  mind  of  the  child. 

5.  Events  should  be  mastered  by  interesting  repeti- 
tion. 

6.  Important  dates  should  be  committed  to  memory 
to  serve  as  bases  for  comparison. 

7.  The  child  should  be  trained  to  recite  the  lesson 
without  prompting  or  questioning. 


HISTORY.  Ill 

II.  Cause  and  Effect. 

Biography  and  events,  which  were  originally  taught 
as  facts,  are  now  made  to  yield  to  a  higher  process  — 
the  recognition  of  cause  and  effect.  But  in  order 
that  the  process  may  be  of  value  as  an  intellectual 
discipline,  the  child  himself  should  be  led  to  draw  the 
inferences. 

III.  Ethics. 

The  good,  the  true,  the  beautiful,  cannot  be  awakened 
into  motive  forces  by  direct  teaching.  Child  nature 
resents  such  an  attempt;  while  the  lessons  taught  in- 
directly by  biography,  by  events,  and  by  institutions 
insinuate  themselves  into  the  mind  and  heart  of  the 
child  and  become  part  of  his  inner  life  —  his  character. 


IX.  —  CIVICS. 

Aim:   Training  in  and  for  citizenship. 

The  teaching  process,  in  order  to  be  successful,  must 
take  into  consideration  the  child  to  be  educated,  the 
material  for  his  education,  and  the  teacher,  who  is  the 
medium  between  the  two,  their  relative  importance 
depending  upon  the  aim  of  the  lesson.  Civics,  which 
seeks  primarily  to  impress  its  principles  upon  the  moral 
sense  of  the  child,  must  necessarily  give  prominence  to 
the  character  of  the  teacher. 

Fundamentals. 
1.    The  child. 

(a)  The  underlying  civic  virtue  is  obedience  to 
constituted  authority ;  hence,  train  the 
child  first  to  a  habit  of  implicit  obedi- 
ence. 

(V)  Obedience  should  aim  to  a  rational  and  vol- 
untary compliance  to  an  inner  authority ; 
hence,  rationalize  the  child's  knowledge  of 
law  and  order,  broaden  and  deepen  his 
sense  of  duty,  and  give  impulse  to  his 
conduct. 

112 


CIVICS.  115 

(<?)  In  intellectual  education,  interest  is  a  con- 
dition to  knowledge ;  in  moral  education, 
knowledge  is  a  condition  to  interest. 

(c£)  The  child  is  in  possession  of  all  the  elemen- 
tary concepts  which  underlie  this  study 
through  intercourse  with  those  with  whom 
he  comes  in  contact  long  before  he  begins 
the  study  of  civics. 

(g)  The  principles  underlying  the  teaching  of 
other  studies  obtain  here  also:  Faith  in 
the  concrete,  reasoning,  conviction,  action, 
are  the  steps  in  the  development  of  a  civic 
character. 

2.    Material. 

(a)  The  purposes  of  government. 

The  material  must  be  concrete  and  familiar  —  the 
home,  as  represented  by  the  head  of  the  family ;  the 
school,  by  the  teacher ;  the  city,  by  the  policeman  and 
the  fireman. 

(7>)  A  knowledge  of  our  form  of  government. 

The  material  should  include  the  leading  facts  and 
the  underlying  principles  of  municipal,  state,  and  fed- 
eral governments. 

(c)  The  duties  of  citizens. 
A  comparison  with  other  forms  of  government   in 


116  CIVICS. 

order  to  emphasize  such  peculiar  institutions  as  suf- 
frage, primaries,  and  conventions. 

((T)   Historical  personages  and  events. 

3.    The  teacher. 

Only  the  teacher  who  is  zealous  in  the  cause  of  good 
citizenship  can  arouse  and  maintain  the  child's  interest 
in  this  study,  can  make  him  appreciate  the  blessings  of 
our  free  government,  can  induce  him  to  feel  that  he 
owes  certain  duties  to  his  citizenship  which  call  for 
cheerful  responses  on  his  part. 

Method. 
Model  Lesson  on  Primaries  (Rights  and  Duties).1 

1.  Facts: 

(a)  Definition. 

(b)  Date. 
(<?)  Location, 
(c?)  Participants, 
(e)  Purpose. 

2.  Relations : 

(a)  To  the  character  of  the  candidates. 

(b)  To  the  character  of  the  government. 

(c)  To  the  moral  tone  of  the  community. 

(d)  To  the  American  idea  of  government. 

(e)  To  self-respect,  and  to  respect  of  others. 

1  Morally,    attendance    upon    pi'imaries    and    voting   are    duties 
legally,  they  are  not  —  the  more's  the  pity! 


CIVICS.  119 

3.  Feelings : 

(a)  Free  government  is  a  heritage  handed  down 
to  us  by  centuries  of  oppression,  suffering, 
and  bloodshed ;  hence  this  right  involves 
a  duty,  for  "  Eternal  vigilance  is  the  price 
of  liberty." 

(6)  Neglect  to  perform  the  duties  of  citizenship 
results  in  political  rings  formed  for  selfish 
purposes  and  dominated  b}r  the  one-man 
power  —  a  travesty  on  our  boasted  self- 
government  ! 

(<?)  Such  conditions  ought  not  to  be  tolerated  by 
enlightened  men,  both  as  individuals,  as 
members  of  society,  and  as  Americans. 

4.  Action : 

The  teacher  can  only  sow  the  seed ;  he  must  leave 
the  rest  to  the  future. 


X.  —  ARITHMETIC. 

Aims : 

1.  Utilitarian. 

2.  Intellectual. 

General  considerations : 

I.  As  a  school  study,  arithmetic  includes  : 

(a)  Examples  which  deal  with  the  fundamental 
processes  of  numbers,  as  2|  ~  1^. 

(6)  Problems,  or  questions  involving  numbers,  in 
which  the  nature  of  the  processes  must  first 
be  determined  by  reasoning,  as,  If  1|  yards 
of  cloth  cost  $2f,  what  will  1  yard  cost? 

II.  The    processes    involved    in    examples    may    be 
learned  in  two  ways  : 

(a)  Through  authority,  as  when  a  child  is  told 
that  to  divide  one  fraction  by  another,  he 
must  invert  the  divisor  and  proceed  as  in 
multiplication. 

(7>)  Through  induction,  or  the  process  whereby 
general  laws  are  obtained  through  the  in- 
vestigation of  particulars,  as,  for  instance, 
when  the  child,  in  comparing  the  results 
of  several  divisions  of  fractions,  formulates 
for  himself  the  law  of  the  division  of 
fractions. 

120 


ARITHMETIC.  123 

III.  Arithmetical  induction  may  be  obtained  in  two 
ways  : 

(a)  By  investigating  the  results  of  several  con- 
crete presentations,  as,  for  example  :  In 
dividing  |  by  -|,  the  child  chooses  a  piece 
of  paper  as  a  unit,  measures  off  |  of  it, 
then  |  of  it ;  then  shows  by  actual  meas- 
urement that  the  result  of  dividing  J  by  | 
is^. 

(b*)  By  abstract  reasoning.  Thus,  the  answer  to 
the  above  might  have  been  obtained  by 
reasoning  in  this  wise  :  Dividing  |  by  \ 
will  give  -X3°-  as  a  quotient,  and  dividing  | 
by  |  will  give  ^  of  J^-  or  ^-  as  a  quotient. 

Fundamentals. 

1.  The  child's  knowledge  of  the  laws  of  arithmetic 
should  be  the  result  of  his  own  inductions. 

2.  Induction  through  the  concrete  is  the  proper 
method  for  fundamental  processes,  and  it  must  precede 
the  abstract  method. 

3.  Concrete  presentation  for  the  purpose  of  induc- 
tion is  demanded  only  by  the  processes  involving  whole 
numbers  and  common  fractions. 

4.  Processes  should  be  mastered  before  an  attempt 
is  made  to  apply  them  to  the  solution  of  problems. 

5.  Oral  arithmetic  is  for  instruction  and  drill ;  writ- 
ten arithmetic,  for  exercises  that  deal  with  large  numbers. 

6.  Induction  should  be  preceded  by  preparation  and 


124  ARITHMETIC. 

followed  by  application,  making  the  whole  a  process  of 
apperception. 

7.    The  type  is  of  great  value  in  arithmetic. 

Method. 

Fundamental  operations  —  integers. 
Guide:   Concrete  presentation. 

Counting. 

1.  Counting  is  regarded  as  the  initial  step  in  arith- 
metic teaching,  because  : 

(a)  It  is  a  process  with  which  the  child  is  already 
acquainted  when  he  enters  school. 

(5)  It  is  the  natural  basis  of  the  fundamental 
operations. 

2.  The  teaching  progression :  idea,  word,  symbol. 
Symbols  are  introduced  thus  early  because  they  embody 
in  concrete  form  the  child's  abstractions,  and  thereby 
assist  in  his  further  progress,  and  because  of  their 
practical  utility. 

Addition. 
Counting  (synthesis). 

1.  To  teach  the  combination,  three  and  two  are  five. 
(a)  Children  are  given,  or  are  told  to  take,  first, 
3  sticks,  and  then  2  sticks.  Questions  fol- 
low with  a  view  to  directing  the  pupils' 
attention  to  the  two  groups  and  their  com- 
positions ;    after    which   they  are    told  to 


ARITHMETIC.  127 

count  the  number  of  sticks  in  both  groups 
(all  together)  ;  and  to  announce  the  result, 
first  as  5  sticks  ;  later,  as  3  sticks  and  2 
sticks  are  5  sticks  ;  and  lastly,  as  3  and  2 
are  5. 

(5)  Represent  the  process  and  the  result  on  the 
blackboard  (symbol  of  formula). 

(c)   Drill. 

2.  15 

23 

The  child  has  on  his  desk  a  bundle  of  10  splints,  and 
to  the  right  of  it  5  splints,  and  below  them  a  piece  of 
paper  on  which  he  has  written  the  number  15.  After 
recognizing  the  figure  which  represents  the  bundle  and 
the  figure  which  represents  the  loose  sticks,  he  adds  8 
splints  to  the  5  splints,  and  writes  the  8  below  the  5. 
Upon  counting  his  loose  splints,  he  finds  that  he  has 
13  of  them,  10  of  which  he  binds  into  a  bundle,  leaving 
3  loose  splints.  The  latter  he  represents  by  a  3  placed 
in  the  units  column;  the  bundle  he  transfers  to  the  left 
(the  transfer  being  marked  on  the  paper),  and  the  two 
bundles  he  represents  by  the  figure  2  placed  in  the 
tens  column. 

Subtraction. 

Counting  (analysis). 

35 

-18 

17 


128  ARITHMETIC. 

The  child  arranges  the  splints  as  in  addition ;  also 
the  paper  on  which  the  bundles  are  represented  by  3, 
and  the  loose  splints  by  5.  He  discovers  that  he  can- 
not take  away  8  splints  when  he  has  only  5  splints,  but 
that  he  can  take  a  bundle  and  transfer  it  as  10  single 
splints  to  the  5  splints.  He  has  now  2  bundles  and  15 
splints  (a  result  which  he  marks  on  his  paper).  From 
the  15  splints  he  takes  awa}'  8  splints,  leaving  7  splints 
(represented  on  the  paper  as  7  units)  ;  and  from  the  2 
bundles  he  takes  1  bundle,  leaving  as  a  remainder  1 
bundle  (represented  on  the  paper  as  1  ten). 

Multiplication. 

Counting  of  equal  numbers  with  reference  to 
"times"  (synthesis). 

To  teach  2 

x  3 
6 

Each  pupil  arranges  3  groups,  each  containing  2 
objects,  then  counts  the  number  of  objects  in  the  3 
groups,  and  announces  that  the  3  groups,  each  contain- 
ing 2  objects,  have  in  all  6  objects.  Next,  he  writes 
three  2's  in  a  column,  adds  them,  and  tells  how  many 
2's  make  6.  This  knowledge  he  now  represents  by  the 
formula  (briefer  by  comparison  than  that  of  addition) 

2 

x  3  k 

6 
and  commits  to  memory. 


ARITHMETIC.  131 

Division. 

Counting  of  equal  numbers  with  reference  to  "-times" 
(analysis).  g,15 

5 

Each  pupil  arranges  his  15  objects  into  groups,  each 
group  containing  3  objects.  He  then  counts  the  num- 
ber of  the  groups  and  announces  that  he  separated  or 
divided  the  15  objects  into  5  groups,  each  containing 
3  objects.  He  next  writes  a  sufficient  number  of  3's  in 
a  column  to  add  up  to  15,  or  he  subtracts  successively 
a  sufficient  number  of  3's  from  15  to  have  no  re- 
mainder. In  either  case  he  finds  that  the  3  has  been 
involved  5  times.     He  now  learns  the  formula 

3[15 
5 
and  commits  its  substance  to  memory. 

Common  Fractions. 
Guides  : 

1.  Concrete  Presentation. 

2.  The  Formal  Steps. 

Method  I. 

Addition. 

1.  Preparation :  Find  fractional  parts  of  whole 
numbers. 

2.  Presentation :  1.   Add  |  and  \. 

The  pupil  is  given  6  objects,  such  as  buttons,  marbles, 
splints,  etc.,  and  required  to  find  J  of  them   and  \  of 


132  ARITHMETIC. 

them  ;  then,  having  found  that  |  of  the  marbles  =  3 
marbles,  and  ^  of  the  marbles  =  2  marbles,  with  proper 
guidance  he  concludes  that  ^  of  the  marbles  +  1  of  the 
marbles  =  -|  of  the  marbles  —  a  conclusion  which  he 
later  transforms  through  abstraction  into  |-  +  ^  ==  |. 

If  he  proceeds  likewise  with  the  following,  and  comes 
to  the  conclusion  that 


2. 

lil-_     7 
2   ^   5  —   10 

3. 

2  J.1..11 

3  ^  4 —   12 

4. 

1  _|_  1  4-1  - 

2  ^  4  ^  5  " 

38 
40' 

he  has  all  the  material  necessary  for  the  third  step. 
3.    Comparison. 

The  Common  Denominator. 

Analysis. 

Example.  Original  denominators.  Common  denominators. 

1.  2,      3  6 

2.  2,      5  10 

3.  3,      4  12 

4.  2,  1,  5  40 1 

1  There  is  no  valid  reason  for  the  custom  of  discontinuing  thus  early 
in  favor  of  the  least  common  denominator  the  idea  that  the  common 
denominator  is  the  product  of  the  various  denominators.  The  argu- 
ments in  favor  of  the  latter  practice  may  be  briefly  stated  as  follows : 

1.  It  does  not  burden  the  pupil  with  too  many  processes  at  the  very 
outset. 

2.  It  leaves  the  fractions  intact. 

3.  The  attention  at  the  very  outset  is  directed  to  the  aim  rather 
than  to  the  preparatory  matter. 

4.  There  is  an  economy  of  energy  and  time  — reduction  of  the 
answer  is  all  that  is  needed. 


ARITHMETIC.  135 

4.  Generalization  : 

The  Common  Denominator  is  the  product  of  the 
several  denominators. 

The  Numerators. 

If  the  pupil's  attention  is  now  directed  to  the  equa- 
tions i  =  |,  1  =  -^,  |  =  T82,  etc.,  a  vague  intimation  of 
which  he  already  has,  he  will  eventually  discover  that 
the  ratio  existing  between  the  denominators  of  each 
equation  is  the  same  as  that  existing  between  their 
numerators ;  nor  will  he  find  great  difficulty  in 
discovering  and  in  formulating  a  rule  for  finding 
the  new  numerators  —  in  other  words,  to  gener- 
alize. 

5.  Application   (see  Fundamental  6): 

Processes  and  concepts  treated  incidentally  in  the  fore- 
going discussion,  or  readily  deducible  from  it. 

1.  Reduction  to  higher  or  lower  terms. 

Corollary  («). 

The  value  of  a  fraction  is  not  altered  when  both 
of  its  terms  are  multiplied  or  divided  by  the 
same  number. 

Corollary  (6). 
Factoring. 

2.  The  need  for  a  common  denominator. 


136 


ARITHMETIC. 


Subtraction  of  Fractions. 

With  the  single  exception  of  the  actual  process  of 
subtraction,  the  mode  of  presenting  this  topic  is  the 
same  as  in  addition. 

Multiplication  of  Fractions. 
Multiply  1  by  l 

Take  6  splints  ;  then 

|  of  6  splints  =  3  splints. 
^  of  3  splints  =  1  splint. 

Proceeding  as  in  addition,  the  conclusion  is  reached 
that 


l  —  I 


X  *  = 


In  the  same  manner, 


Comparison  : 

2 
3 

2 

5 

X 
X 

2 

5  — 

4   - 

6  — 

4 
15* 

8 
3  0' 

Original  numerators. 

Resulting  numerators. 

1,1 

1 

2,2 

4 

2,4 

8 

Conclusion  : 

Original  denominators. 

Resulting  denominators. 

2,  3 

6 

3,  5 

' 

15 

5,  6 

30 

Generalization  : 

To 

m 

ul1 

:iply 

one 

fraction  by  another 

fraction, 

ARITHMETIC.  139 

Division  of  Fractions. 


Divide  ^  by  \. 

Take  6  marbles  ;  then 


Other  examples: 


I  of  6  =  2. 

J  of  6  =  3 1  and 

1  _^  1  —  2 
3    -    2  —  3' 


3  _:_  1  —  6 

y  •  y—  y 

2  _:_  3  _    8_ 
5    *    4  —  15' 

3  _s_  2.  —  9 


Comparison: 

1      i  _=_  i  —  2 

x'      3     *    2  —  3* 

9  3    _;_   1     _    6 

Q        2j.3_J 
°*      5    *    4  —   15* 
4.         3  _;_   2   _    9 

A  few  well-directed  questions  will  reveal  to  the  child 
that  8,  the  numerator  of  the  answer  to  example  3,  for 
instance,  is  the  product  of  4  and  2,  and  that  15,  the 
denominator  of  the  same  answer,  is  the  product  of  3 
and  5.     Likewise  with  the  other  examples. 

Generalization:  The  law  governing  the  division  of 
fractions. 

Application : 

1  Attention  must  be  called  at  this  point  to  the  change  of  base  which 
takes  place  in  multiplication,  but  not  in  division  of  fractions.  A  com- 
parison of  the  two  processes  will  make  this  point  clear. 

Multiply  \  x  \.  Divide  \  by  \. 


A  of  6  [base]  =  2. 
\  of  2  [new  base]  =  1. 

.     1    v   1  —  1 

•  •  3  A  2  —  6* 


i  of  6  [base]  =  2. 
|  of  0  [same  base]  =  3. 

.      1   j_   1   —   2 

•  •   3     •     5  —   3* 


140 


ARITHMETIC. 


Method   II. 

(For  more  advanced  pupils.) 

The  presentation  step  only  will  be   discussed  here. 
The  rest  have  already  been  discussed  in  Method  I. 


1 4- 1 

9.  T^  8" 


Addition. 


AD  is  the  unit,  AF  is  |  of  it,  and  EH  is  |  of  it, 
and  the  question  becomes:  What  part  of  AD  are 
AF+EH? 

Assuming  GD1  as  the  standard  of  comparison,  or 
the  unit  of  measure,  it  will  be  found  by  actual  meas- 
urement that  AF=S  x  GD,  and  EH=2x  GD;  or 
that  GD  is  contained  2  times  in  EH,  and  3  times  in 
AF.  AD  is  thus  seen  to  be  divided  into  6  equal  parts, 
of  which  AF  contains  3  and  EH,  2. 

Sothafi+i  =  t  +  |  =  f. 


1  In  case  the  figure  contains  no  exact  unit  of  measure,  one  can 
be  obtained  by  dividing  its  smallest  division  into  2  parts,  or  3  parts, 
etc. 


ARITHMETIC. 


143 


Subtraction. 


1  _1 

2  3" 


A 

G                  E 

C 

; 

"ll 

:                  3 

« 

B 

H                 F 

D 

AD  is  the  unit,  AF  is  -|-  of  it,  AH  is  \  of  it. 

The  difference  between  AF  and  AH  is  evidently  GF, 
and  the  question  becomes:   What  part  of  AD  is  GF ? 

Assuming  GF  as  the  unit  of  measure,  and  proceed- 
ing as  in  addition,  we  have  ^  —  ^  =  §  —  |  =  ^ . 


x 


Multiplication. 


AGE 

C 

"ivivXviv'v;':';^: 

V 

111 

ill 

B                 t 

H                 F 

D 

AD  is  the  unit,  AF  is  1  of  it,  and  AH  is  J-  of  AF,1 
and  the  question  becomes:  What  part  of  AD  is  AH? 
Evidently  1. 


So  that  ixl=  J, 


1  See  note  to  Method  I. 


144 


ARITHMETIC. 
Division. 


1  J.  1 

2    '    3* 

A 

G 

E 

c 

lllllllliilil 

H 

ISIlillB 

^SSSSS 

B  H  F  D 

AD  is  the  unit,  AF  is  J  of  it,  J.IT  is  J  of  it,  and  the 
question  becomes :  How  many  times  is  AH  contained 
in  AF,  or  how  does  AF  compare  in  size  to  AH,  or  what 
part  ol  AHis  AF? 

Assuming  GF  as  the  unit  of  measure,  and  proceed- 
ing as  previously,  we  find  that  AF  is  composed  of  3 
units,  and  AH  of  2  units;  so  that  AF  is  §  of  AH,  or 
.Ajffis  contained  l1-  times  in  AF. 

Hence  ^  -s-  ^  =  §. 

Numeration  and  Notation  of  Decimals. 

Guide :   Common  fractions. 

Preparation:  The  number  of  places  an  integer  of 
any  given  value  requires  for  its  notation. 

Presentation:  Notation  of  decimals,  although  it  de- 
pends upon  the  device  of  place,  can  still  be  made  the 
subject  of  inference,  after  the  first  few  initial  steps  have 
been  mastered  by  the  child, 

For  instance,  if  a  child  has  learned  to  recognize  and 
to  write  such  fractions  as  .3,  .04,  .45,  he  can  be  led  to 


ARITHMETIC.  147 

recognize  the  generalizations  of  both  processes  and  to 
apply  them.     Thus  he  has  already  learned : 

1.  The  denominator  of  a  decimal  fraction  is  indi- 
cated by  a  point  before  the  numerator. 

2.  That  the  device  of  place  indicating  the  cipher  is 
the  same  as  in  whole  numbers. 

3.  That  numbers  are  regarded  as  increasing  toward 
the  left  and  vice  versa  in  a  tenfold  ratio. 

4.  That,  counting  the  decimal  point  as  a  "place," 
there  are  just  as  many  places  needed  to  write  a  decimal 
fraction  as  a  whole  number  of  like  character. 

Application : 

Express  decimally  four  thousand  ninety-eight  hun- 
dred thousandths. 
Explanation : 

Since  hundred-thousandths  requires  6  places,  and  four 
thousand  ninety-eight  takes  up  4  of  the  places,  there 
still  remain  2  places  which  should  be  filled  by  the  deci- 
mal point  and  a  cipher.  Hence,  beginning  with  the 
decimal  point,  the  fraction  is  expressed  as 

.04098. 
The  method  proposed  here  is  recommended  because 
(a)  It  makes  no  distinction  between  whole  numbers 
and  decimal  fractions  in  the  matter  of  place 
value. 
(5)   It  starts  with  the  decimal  point  in  notation  —  of 
great  value  when  fractions  are  dictated  for  the 
purposes  of  addition  or  subtraction. 


148  ARITHMETIC. 


Reduction  of  Decimals. 
Reduce  f  to  thousandths. 


I  is  the  same  as  3  -h  8 

oo 

00 

.375 


9    .    si  —  3  0  _^  Q  —  3  0  0.  _i_  Q  _  3  0  0  0  _.    Q  _  _3JL§_ 
o    .    o—  10    .    o—  1Q0    .    o-  1000    .    o—  1000 


or,  decimally, 


8  3.000 


Multiplication  of  Decimals. 

Decimals  being  merely  a  device,  the  laws  governing 
its  fundamental  operations  should  be  taught  by  refer- 
ence to  common  fractions,  thus : 

-1-  x  -1-  —  _L_        •      1  x    1  —   01 

10A10—  100'        *  *    -iA.x  —  .vx. 

-2-4-  x  -8-  —  -2_i_g_       .     24  x    9  =   216   etc 
100  A  10  ~  1000'       ••    •  -*  *  -^  —  ■*diui  Cl,u 

Hence  the  rule  :  Point  off  in  the  product  as  many 
figures  from  the  right  as  there  are  decimal  figures  in 
the  multiplicand  and  the  multiplier. 

Division  of  Decimals. 
(When  the  divisor  is  an  integer.) 

.3 

1      _9_  -i.  3  —  _9_  v  1  =  _§_         •    3|  Q* 


2     -K  —  3  —  — 9—  x  1  =  -&-       •    3fOQ* 

*•      100    •    J—  100*3100"      ••°|-vC 


.0003 


a a =-  s  =  —9 x  i  = s. •  3  oooq 

°*    ioooo  •  °~  ioooo  A  3      loooo1    ••  °I-UUUJ 

Conclusion  :  The  number  of  decimal  places  in  the 
quotient  is  the  same  as  the  number  of  decimal  places  in 
the  dividend. 


ARITHMETIC.  151 

(When  the  divisor  is  a  fraction.) 

...  .3(9=  3 [90. 

2.  9  -  t|-q  =  9  x  ijp  =  J4P-  =  900  -  3. 

.•.  .03[9  =  3|900. 

3.  9_s.T^  =  9  xi-°3°-0  =  ^n  =  9000 -3. 

.-.  .003[9  =  3|9000. 

Conclusion  :  We  can  get  rid  of  a  fractional  divisor 
by  multiplying  both  the  divisor  and  the  dividend  by 
the  denominator  of  the  divisor. 

Deduction:  Divide  .009  by  .03.  o 


.03|.009  =  3p9;  or,  briefly,  x  03. |  x  00.9 

Prnnf  • 9 ...      3     —  __9 v  100  —  _3_ 

x  i  uuj.  .     1000-    •    !  o  o  —  1000   A      3      —  10* 

Percentage. 

Some  of  the  difficulties  which  children  encounter  here 
will  be  obviated  by  defining  "  rate  per  cent "  as  so  many 
out  of  each  hundred.  Thus  §fo  means  6  out  of  a  hun- 
dred ;  6<?o  of  $500  means  $6  out  of  each  $100  ;  Ifo  of 
800  sheep  means  7  sheep  out  of  each  group  of  100  sheep. 

Analysis  is  the  basic  method  in  percentage. 

Examples  : 

1.    Find  bfi  of  $800. 

lfioi  $800  =  $8o 
5fo  of  $800  =  $40, 


152  ARITHMETIC 

or  88.00 

5 

$40.00 

2.    What  per  cent  of  200  is  8  ? 

If  of  200  =  2. 

.-.  8  =  4'/o. 

Interest. 

With  the  360  days  method,  the  new  factor  presents 
but  little  difficulty. 

Example  : 

Interest  on  $500  for  1  yr.  2  mos.  12  days  at  4|^>. 

$500  x  432  x  9  = 
360  x  200 

Proportion. 

Problems  included  under  this  topic  should  be  solved 
by  analysis,  as  follows  : 

If  4  men,  working  9  hrs.  a  day,  require  2  days  to 
build  a  wall  18  ft.  high,  how  many  days  will  6  men,  work- 
ing 8  hrs.  a  day,  require  to  build  a  wall  12  ft.  high  ? 

Analysis  : 

(a)  If  4  men  require  2  days, 

1  man  requires  4x2  days, 

6  men  require  -  of  4  x  2  days, 
6 

or  4x2   , 

—  days. 


ARITHMETIC.  155 

4x2 

(b)    If  6  men  require  — - —  days  to  build  18  ft., 

they  will  require  —  of  — —    days  to  build 

1  ft.  and  12  x  —   of days  to  build 

18  6  J 

12  ft. 

12  x  4  x  2    , 

°r  -181T6-  dayS' 

(<?)    If  6  men,  building  a  wall  12  ft.  and  working 

0  i  i  •       12x4x2, 

9  hrs.  a  day,  require  — — — —  days, 

if  they  work  1  hr.  a  day,  they  will  require 

Q      12x4x2   , 

9  X  "18^3-  dayS' 

and  working  8  hrs.  a  day,  they  will  require 

1  ,Q      12x4x2   , 
8°f9x-18T6-dayS' 

9x12x4  x2   , 

or     —7^ — T7, tt~  days. 

8  x  18  x  6  J 

Square  Root. 
First  Step  :   Preparation. 

(a)  The  notion  of  square  root  is  obtained  by  such 
exercises  as  3x3=9,  9  x  9  =  81,  12x12  =  144,  in 
which  the  product  of  the  two  equal  factors  is  the 
square,  and  one  of  the  two  equal  factors  is  the  square 
root.     Square  and  square  root  are  thus  seen  to  be  rela- 


156 


ARITHMETIC. 


tive  terms.  Square  root  cannot  be  taught  without 
reference  to  its  square,  nor  can  the  latter  be  conceived 
apart  from  the  former. 

(6)  The  symbols,  52,  V25. 

(c)  The  terms  "  power,"  "  involution,"  "  evolution," 
"index,"  "radix." 

(<i)  The  analytic  method  of  squaring  numbers.  As 
this  topic  does  not  engage  the  pupil's  attention  before 
he  has  reached  a  point  in  his  mental  development  when 
he  is  already  in  possession  of  the  elementary  knowledge 
that  underlies  its  elaboration,  or  before  he  can  interpret 
the  words  of  his  teacher  in  terms  of  individualized  or 
experienced  notions,  this  method  is  preferable  to  the 
synthetic. 

The  process  of  squaring  any  number,  as,  for  ex- 
ample, 25,  may  be  presented  under  three  different 
operations. 

(a) 

Which  is  the  ordinary  method 
of  multiplication. 


(&) 


25 

25 

125 

50 

of 

625 

25 

25 

25  =  5  x  5,  or  52 

100  =  20  x  5 

100  =  20x5 

400  =  20  x  20  or  202 

625 


Which  shows  the  opera- 
tion in  full. 


ARITHMETIC. 


159 


0)            20  +  5 

20  +  5 

20  x  5  +  52 

202  +  20  x  5 

202  +  2(20  x5)  +  52  = 

=  625 

Which  differs  from 
b  only  in  expressing 
the  +  symbol. 


(c?)  Again, 


(0  Or 


252  =  (23  +  2)2  =  625 

23  +  2 

23  +  2 

23  x  2  +  22 

232  +  23  x  2 

232  +  2(23  x  2)  +  22  =  625 

252=(7  +  18)2=625 
7  +  18 

7  +  18 

7  X18  +  182 

72  +  7xl8 

72  +  2(7  xl8)  +  182=625 


That  is,  the  square  of  any  number  =  the  square  of 
any  two  numbers  whose  sum  equals  that  number  + 
twice  the  product  of  those  numbers. 


(/)  Lastly, 


(20  +  5)2=20  +  5 
20  +  5 


202+20x5 
+  20  x  5  +  r>2 


202+2(20  xo)  +  52=G25 


160  ARITHMETIC. 

In  other  words,  the  validity  of  the  process  and  of  the 
answer  is  in  nowise  affected  when  the  process  of  multi- 
plication begins  with  the  numbers  to  the  left  of  the 
plus  sign. 

If,  for  the  sake  of  brevity,  we  represent  the  number 
to  the  left  of  the  plus  sign  by  x,  and  the  number  to  the 
right  of  it  by  y,  the  process  of  involution  (when  the 
number  is  composed  of  two  component  parts)  may  be 
represented  as, 

(x  +  y)2  =  x2  +  2  xy  +  y2. 

A  good  rule  to  follow  is  not  to  consider  the  prepara- 
tion completed  unless  the  child  recognizes,  as  the  result 
of  his  own  efforts  : 

1.  That  evolution  is  primarily  a  process  of  division; 

2.  That  the  process  of  extracting  the  square  root 
may  begin  either  at  the  right  or  at  the  left ; 

3.  That  the  algebraic  expression  is  a  symbolic  repre- 
sentation of  a  general  truth  which  he  can  demonstrate 
satisfactorily ;  and 

4.  That  the  number  may  be  divided  into  periods 
containing  any  number  of  figures. 


ARITHMETIC.  163 

Example: 

Find  the  square  root  of  54756. 

Beginning  at  the  right,  and  pointing  off  periods  of 
one  figure,  we  have, 

1.  2  +  5  +  20  +  41  +  166  =  234 
5,  4,  7,  5,  6  =  x2  +  2  xy  +  y2 

4  =  y" 

52  =  x2  +  2  ry 
2x2x5)  + 5x5)        45  =  f 

7Q7  =  x2  +  2xy 

2  x  7  x  20)  +  20  x  20)       680  =  y2 

4027  =  z2  +  2  ^ 
2  x  27  x  41)  +  41  x  41)     3895  =  y2 

50132  =  x2  +  2xy 
2  x  68  x  166)  +  166  x  166)  50132  =  x2  +  2  xy 

2.  Beginning  at  the  right  and  pointing  off  periods 
of  two  figures: 

7  +  61  +  166  =  234 

5,  47,  56  =  x2  +  2  xy  +  y2 

49  =  y2 


±101  =  x2  +  2xy 
2x7  x61)  +  61  x61)     4575  =  y2 


5Q132  =  x2  +  2xy 
2  x  68  x  166)  +  166  x  166)  50132  =  x2  +  2  ^ 


1C4  ARITHMETIC. 

Second  Step :   Presentation. 

The    following    method    is   then   shown   to   be    the 
simplest. 

Find  the  square  root  of  978121. 

+  9     : 
+  80     :     989 
900     : 
978121 
900x900  =  810000 


=  168121 

2  x  900  x  80)  +  80  x  80)  =  150400 

=    17721 
2x980x9) +  9x9)=    17721 

Third  Step :   Comparison. 

Comparison  of  several  examples  of  like  character  to 
above  will  make  evident  the  following  facts : 

1.  That,  when  a  quantity  is  expressed  by  an  even 
number  of  figures,  its  square  root  contains  one  half  its 
number  of  figures ;  but  when  a  quantity  is  expressed 
by  an  odd  number  of  figures,  its  square  root  con- 
sists of  one  more  than  one  half  its  number  of  figures. 
This  principle  may  also  be  demonstrated  by  involution. 

2.  That  the  subtrahend  (with  the  possible  exception 
of  the  initial  and  the  final)  contains  an  even  number 
of  zeros. 

3.  That  (with  the  single  exception  of  the  initial  sub- 
trahend, which  involves  either  one  or  two  figures,  de- 


ARITHMETIC.  167 

pending  upon  whether  the  square  is  made  up  of  an 
even  or  of  an  odd  number  of  figures)  two  figures  of  the 
minuend  are  successively  involved  in  finding  the  square 
root  corresponding  to  the  given  period. 

4.  That  the  sum  of  the  products  of  two  multiplica- 
tions, both  having  the  same  number  as  a  multiplier, 
equals  the  product  of  the  sum  of  the  multiplicands  by 
the  multiplier ;  as,  for  example, 

9x5  +  5x5  =  14  x  5. 

Fourth  Step :  Generalization. 

The  aim  of  the  lesson  is  best  served  by  leading  the 
child  to  frame  rules,  rather  than  to  allow  him  to  memo- 
rize the  rules  found  in  the  text-book. 

Fifth  Step :    Application. 

(a)  Find  the  square  root  of  54756  and  of  numerous 
other  examples  as  follows  : 


2     3 

4 

5,  47, 

56 

4 

43) 
64) 

147 
129 

1856 
1856 

(5)  Solve  the  following  and  similar  problems : 

A  man  owns  a  farm  in  the  form  of  a  square  which 

contains  45  A.  25  sq.  rd.     How  many  rods  in  length  or 

breadth  is  it  ? 


A  History  of  Education  in  the 
United  States 

By  EDWIN   GRANT  DEXTER,  Ph.D. 

Professor  of  Education  in  the  University  of  Illinois 
$2.00  net 

This  new  work  has  been  prepared  in  the  belief  that  the  greatest  need  of  the 
student  of  our  educational  history  is  a  considerable  mass  of  definite  fact  upon 
which  to  base  his  own  generalizations,  or  with  which  to  interpret  those  of  others, 
rather  than  extended  philosophical  discussions  of  historical  trend.  Current 
educational  literature  is  rich  in  the  latter,  though  comparatively  barren  of  the 
former.  The  present  book  deals,  therefore,  with  the  fact  rather  than  with  the 
philosophy  of  education  in  the  United  States.  It  contains  an  exceptionally 
valuable  equipment  of  references  and  bibliographies. 


The  Philosophy  of  Education 

By  HERMAN   HARRELL  HORNE,    Ph.D. 

Assistant  Professor  of  Philosophy  and  Pedagogy  in  Dartmouth  College 

$1.50  net 

This  volume  is  a  connected  series  of  discussions  on  the  foundations  of  edu- 
cation in  the  related  sciences  of  biology,  physiology,  sociology,  psychology,  and 
philosophy.  It  is  not  another  of  the  many  current  manuals  of  practice,  but  a 
thoroughgoing  interpretation  of  the  nature,  place,  and  meaning  of  education 
in  our  world.  The  newest  points  of  view  in  the  realms  of  natural  and  mental 
science  are  applied  to  the  understanding  of  educational  problems.  The  field  of 
education  is  carefully  divided,  and  the  total  discussion  is  devoted  to  the  philos- 
ophy of  education,  in  distinction  from  its  history,  science,  and  art.  The  con- 
ceptions of  evolution,  society,  and  genetic  psychology  shed  their  light  upon 
educational  phenomena,  yielding  in  the  end  a  comprehensive  definition  of  what 
education  is.  The  various  conflicting  modern  educational  opinions  are  organ- 
ized to  a  considerable  extent,  and  are  made  to  appear  as  partial  truths  of  a 
common  system.  The  whole  is  suffused  with  the  spirit  of  an  idealistic  philos- 
ophy in  which  education  is  finally  made  to  yield  its  ultimate  meaning  as  to  the 
origin,  nature,  and  destiny  of  man. 


THE    MACMILLAN    COMPANY 

64-66  FIFTH  AVENUE,   NEW   YORK 


METHODS  OF   ELEMENTARY  EDUCATION 


By  DR.  CHARLES  A.   McMURRY 
COVERING  ALL  GRADES  OF  THE  COMMON  SCHOOL 


THE  ELEMENTS   OF   GENERAL   METHOD      . 
THE   METHOD   OF   THE   RECITATION  (By  C.  A.  and 
F.  M.  McMurry) 

SPECIAL  METHOD  IN  THE  READING  OF  COM- 
PLETE ENGLISH   CLASSICS       .... 

SPECIAL  METHOD  IN  PRIMARY  READING  AND 
ORAL   WORK   WITH   STORIES    .... 

SPECIAL  METHOD   IN   GEOGRAPHY 

SPECIAL   METHOD  IN   HISTORY      .... 

SPECIAL   METHOD   IN   ELEMENTARY   SCIENCE  . 

SPECIAL    METHOD   IN   ARITHMETIC 


90  cents 

90  cents 

75  cents 

60  cents 
70  cents 
75  cents 
75  cents 


IN  PREPARATION 

SCIENCE   LESSONS   FOR   PRIMARY  GRADES 
SPECIAL    METHOD    IN    MANUAL    TRAINING    AND    CON- 
STRUCTIVE  WORK 
SPECIAL   METHOD  IN   LANGUAGE 


TWO    NEW    BOOKS    ON    GEOGRAPHY 

By  Dr.  Charles  A.  McMurry 

EXCURSIONS    AND   LESSONS    IN   HOME   GEOGRAPHY 
TYPE  STUDIES  FROM  THE  GEOGRAPHY  OF  THE  UNITED 
STATES.     Each  50  cents,  net. 

Two  new  books  for  the  use  of  both  teachers  and  pupils.  The  material 
provided  in  the  Excwsions  and  Lessons  constitutes  the  introductory  lessons 
in  geography  for  third  and  fourth  grades.  It  is  the  geography  of  the  home 
and  the  neighborhood.  The  illustrations  are  taken  from  many  different 
localities,  and  are  typical  of  various  parts  of  the  country. 

Type  Studies  is  designed  to  illustrate  in  some  detail  the  second  stage  of 
geography  study,  following  the  Excursions  and  Lessons.  The  puipose  of  the 
simple  tvpe  studies  given  is  to  introduce  children  to  the  geography  of  our 
own  country.    This  volume  also  is  appropriately  illustrated. 


BUTLER'S  THE  MEANING  OF  EDUCATION  .         .     $1.00 

CHUBB'S  THE  STUDY  AND  TEACHING  OF  ENG- 
LISH        i.oo  net 

CUBBERLEY'S  SYLLABUS  OF  HISTORY  OF  EDU- 
CATION .         ........       2.60  net 

DE   GARMO'S   INTEREST   AND  EDUCATION        .       1. 00  net 

DUTTON'S   SOCIAL  PHASES   OF  EDUCATION     .       1.25 

HANUS'S   EDUCATIONAL   AIMS   AND   VALUES  .        1.00 

HERBART'S  OUTLINES  OF   EDUCATIONAL  DOC- 
TRINE     1.25  net 

HERRICK'S   THE  MEANING  AND  PRACTICE  OF 

COMMERCIAL  EDUCATION        ....       1.25  net 

KING'S   PERSONAL  AND   IDEAL   ELEMENTS  IN 

EDUCATION 1.50  net 

KIRKPATRICK'S     FUNDAMENTALS     OF     CHILD 

STUDY 1.25  net 

MONROE'S    SOURCE    BOOK    OF    THE    HISTORY 

OF  EDUCATION 2.25  net 

OPPENHEIM'S     MENTAL    GROWTH    AND    CON- 
TROL       1.00  net 

DEVELOPMENT  OF  THE  CHILD  .        .         .       1.25  net 

REDWAY'S   THE   NEW  BASIS    OF    GEOGRAPHY       1,0c  net 

ROWE'S     THE     PHYSICAL     NATURE     OF     THE 

CHILD .  1.00 

ROYCE'S  OUTLINES  OF  PSYCHOLOGY  .         .         .       i.oo  net 

SHAW'S   SCHOOL  HYGIENE 1.0c  net 

SMITH'S  TEACHING  OF  ELEMENTARY  MATHE- 
MATICS   1.00  net 

3 


A    MODERN    SCHOOL 

$1.25  Net 

By  PAUL  H.  HANUS 

Professor  of  the  History  and  Art  of  Teaching  in  Harvard  University 
Author  of  "Educational  Aims  and  Educational  Values"  etc. 

The  chapters  of  which  this  volume  consists,  except  the  last,  deal 
with  various  phases  of  one  central  theme :  the  scope  and  aims  of  a 
modern  school,  and  the  conditions  essential  to  its  highest  efficiency. 
The  last  chapter  offers  some  testimony  on  the  working  of  the  elective 
system, — a  contemporary  question  of  great  importance  to  both  schools 
and  colleges,  —  but  the  testimony  offered  pertains  only  to  the  college. 
The  first  chapter  deals  specifically  with  the  secondary  school;  and  in 
it  the  author  has  endeavored  to  extend  and  strengthen  certain  concep- 
tions set  forth  in  his  earlier  book.  The  next  seven  chapters  contain  a 
fuller  treatment  of  certain  topics  than  was  appropriate  or  expedient  in 
the  first  chapter,  and  discuss  the  internal  and  external  conditions  essen- 
tial to  a  high  degree  of  success  in  the  work  of  any  school. 

PIONEER    HISTORY  STORIES 

PIONEERS  ON   LAND  AND  SEA  ~|       40 

PIONEERS  OF  THE  MISSISSIPPI  VALLEY  \  cents 

PIONEERS  OF  THE   ROCKY  MOUNTAINS  AND  THE  WEST  J     each 

By  DR.  CHARLES  A.  McMURRY 

This  series  provides  excellent  supplementary  reading  matter  for 
schools  of  from  the  fifth  to  the  eighth  grade.  In  these  volumes  is  told 
the  story  of  the  pioneer  life  of  all  sections  of  our  country,  from  the 
epoch-making  voyages  of  Columbus  to  Major  Powell's  marvellous  jour- 
ney through  the  Grand  Canon  of  the  Colorado.  The  stories  are  com- 
plete and  interesting,  making  the  experiences  of  pioneer  life  as  graphic 
and  real  as  possible.  Indeed,  the  text  is  made  up  largely  of  source 
materials.  These  narratives,  which  are  accompanied  by  admirable 
maps  and  illustrations,  constitute  the  best  of  all  introductions  for  chil- 
dren to  the  history  and  geography  of  the  country. 


THE   MACMILLAN    COMPANY 

64-66  Fifth  Avenue,  New  York 
CHICAGO  BOSTON  ATLANTA  SAN  FRANCISCO 

4 


